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We construct the spin-projection operators for a theory containing a symmetric two-index tensor and a general three-index tensor. We then use them to analyse, at linearized level, the most general action for a metric-affine theory of gravity with terms up to second order in curvature, which depends on 28 parameters. In the metric case we recover known results. In the torsion-free case, we are able to determine the most general six-parameter class of theories that are projective invariant, contain only one massless spin 2 and no spin 3, and are free of ghosts and tachyons., Comment: 39 pages. Ancillary notebook with spin projectors is provided separately. Requires the package xTensor for Mathematica v2: references added, some minor corrections

We present exact solutions to Vasiliev's bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are infinite dimensional higher-spin extensions of spacetime isometries generated by six Killing vectors. The solutions presented are obtained by using a method of holomorphic factorization in noncommutative twistor space and gauge functions. In interpreting the solutions in terms of Fronsdal-type fields in spacetime, a field-dependent higher spin transformation is required, which is implemented at leading order. To this order, the scalar field solves Klein-Gordon equation with conformal mass in (anti) de Sitter space. We interpret the FRW solution with de Sitter asymptotics in the context of inflationary cosmology and we expect that the domain wall and FRW solutions are associated with spontaneously broken scaling symmetries in their holographic description. We observe that the factorization method provides a convenient framework for setting up a perturbation theory around the exact solutions, and we propose that the nonlinear completion of particle excitations over FRW and domain wall solutions requires black hole-like states., Comment: 63 pages

Just as string T-duality originates from transforming field equations into Bianchi identities on the string worldsheet, so it has been suggested that M-theory U-dualities originate from transforming field equations into Bianchi identities on the membrane worldvolume. However, this encounters a problem unless the target space has dimension $D = p + 1$. We identify the problem to be the nonintegrability of the U-duality transformation assigned to the pull-back map. Just as a double geometry renders manifest the $O(D,D)$ string T-duality, here we show in the case of the M2-brane in $D = 3$ that a generalised geometry renders manifest the $SL(3) \times SL(2)$ U-duality. In the case of M2-brane in $D=4$, with and without extra target space coordinates, we show that only the ${\rm GL}(4,R)\ltimes R^4$ subgroup of the expected $SL(5,R)$ U-duality symmetry is realised., Comment: 26 pages

Gauged N=8 supergravity in four dimensions is now known to admit a deformation characterized by a real parameter $\omega$ lying in the interval $0\le\omega\le \pi/8$. We analyse the fluctuations about its anti-de Sitter vacuum, and show that the full N=8 supersymmetry can be maintained by the boundary conditions only for $\omega=0$. For non-vanishing $\omega$, and requiring that there be no propagating spin s>1 fields on the boundary, we show that N=3 is the maximum degree of supersymmetry that can be preserved by the boundary conditions. We then construct in detail the consistent truncation of the N=8 theory to give $\omega$-deformed SO(6) gauged N=6 supergravity, again with $\omega$ in the range $0\le\omega\le \pi/8$. We show that this theory admits fully N=6 supersymmetry-preserving boundary conditions not only for $\omega=0$, but also for $\omega=\pi/8$. These two theories are related by a U(1) electric-magnetic duality. We observe that the only three-point functions that depend on $\omega$ involve the coupling of an SO(6) gauge field with the U(1) gauge field and a scalar or pseudo-scalar field. We compute these correlation functions and compare them with those of the undeformed N=6 theory. We find that the correlation functions in the $\omega=\pi/8$ theory holographically correspond to amplitudes in the U(N)_k x U(N)_{-k} ABJM model in which the U(1) Noether current is replaced by a dynamical U(1) gauge field. We also show that the $\omega$-deformed N=6 gauged supergravities can be obtained via consistent reductions from the eleven-dimensional or ten-dimensional type IIA supergravities., Comment: 38 pages, one figure

We compute the one-loop beta functions of the cosmological constant, Newton's constant and the topological mass in topologically massive supergravity in three dimensions. We use a variant of the proper time method supplemented by a simple choice of cutoff function. We find that the dimensionless coefficient of the Chern-Simons term, $\nu$, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on $\nu$; we study analytically the structure of the flow and its fixed points in the limits of small and large $\nu$., Comment: 36 pages. References added

Gauged off-shell Maxwell-Einstein supergravity in six dimensions with N=(1,0) supersymmetry has a higher derivative extension afforded by a supersymmetrized Riemann squared term. This theory admits a supersymmetric Minkowski x S^2 compactification with a U(1) monopole of unit charge on S^2. We determine the full spectrum of the theory on this background. We also determine the spectrum on a non-supersymmetric version of this compactification in which the monopole charge is different from unity, and we find the peculiar feature that there are massless gravitini in a representation of the S^2 isometry group determined by the monopole charge., Comment: typos corrected

We construct N=1 supersymmetrisations of some recently-proposed theories of critical gravity, conformal gravity, and extensions of critical gravity in four dimensions. The total action consists of the sum of three separately off-shell supersymmetric actions containing Einstein gravity, a cosmological term and the square of the Weyl tensor. For generic choices of the coefficients for these terms, the excitations of the resulting theory around an AdS_4 background describe massive spin-2 and massless spin-2 modes coming from the metric; massive spin-1 modes coming from a vector field in the theory; and massless and massive spin-3/2 modes (with two unequal masses) coming from the gravitino. These assemble into a massless and a massive N=1 spin-2 multiplet. In critical supergravity, the coefficients are tuned so that the spin-2 mode in the massive multiplet becomes massless. In the supersymmetrised extensions of critical gravity, the coefficients are chosen so that the massive modes lie in a "window" of lowest energies E_0 such that these ghostlike fields can be truncated by imposing appropriate boundary conditions at infinity, thus leaving just positive-norm massless supergravity modes., Comment: 29 pages

Magical supergravities are a very special class of supergravity theories whose symmetries and matter content in various dimensions correspond to symmetries and underlying algebraic structures of the remarkable geometries of the Magic Square of Freudenthal, Rozenfeld and Tits. These symmetry groups include the exceptional groups and some of their special subgroups. In this paper, we study the general gaugings of these theories in six dimensions which lead to new couplings between vector and tensor fields. We show that in the absence of hypermultiplet couplings the gauge group is uniquely determined by a maximal set of commuting translations within the isometry group SO(n_T,1) of the tensor multiplet sector. Moreover, we find that in general the gauge algebra allows for central charges that may have nontrivial action on the hypermultiplet scalars. We determine the new minimal couplings, Yukawa couplings and the scalar potential., Comment: 42 pages, Latex file; References added, typos corrected, minor clarifications in the introduction and conclusion sections added. Version to be published in Nuclear Physics B

We construct a family of chiral anomaly-free supergravity theories in D=6 starting from D=7 supergravity with a gauged noncompact R-symmetry, employing a Horava-Witten bulk-plus-boundary construction. The gauged noncompact R-symmetry yields a positive (de Sitter sign) D=6 scalar field potential. Classical anomaly inflow which is needed to cancel boundary-field loop anomalies requires careful consideration of the gravitational, gauge, mixed and local supersymmetry anomalies. Coupling of boundary hypermultiplets requires care with the Sp(1) gauge connection required to obtain quaternionic Kahler target manifolds in D=6. This class of gauged R-symmetry models may be of use as starting points for further compactifications to D=4 that take advantage of the positive scalar potential, such as those proposed in the scenario of supersymmetry in large extra dimensions., Comment: 43 pages, plain Latex; Clarification of discussion and references added

We obtain a three-parameter family of massive N=1 supergravities in three dimensions from the 3-sphere reduction of an off-shell N=(1,0) six-dimensional Poincare supergravity that includes a curvature squared invariant. The three-dimensional theory contains an off-shell supergravity multiplet and an on-shell scalar matter multiplet. We then generalise this in three dimensions to an eight-parameter family of supergravities. We also find a duality relationship between the six-dimensional theory and the N=(1,0) six-dimensional theory obtained through a T^4 reduction of the heterotic string effective action that includes the higher-order terms associated with the supersymmetrisation of the anomaly-cancelling \tr(R\wedge R) term., Comment: Latex, 32 Pages, an equation is corrected, a few new equations and a number of clarifying remarks are added

We construct superconformal gauged sigma models with extended rigid supersymmetry in three dimensions. Those with N>4 have necessarily flat targets, but the models with N \leq 4 admit non-flat targets, which are cones with appropriate Sasakian base manifolds. Superconformal symmetry also requires that the three dimensional spacetimes admit conformal Killing spinors which we examine in detail. We present explicit results for the gauged superconformal theories for N=1,2. In particular, we gauge a suitable subgroup of the isometry group of the cone in a superconformal way. We finally show how these sigma models can be obtained from Poincare supergravity. This connection is shown to necessarily involve a subset of the auxiliary fields of supergravity for N \geq 2., Comment: 39 pages

We calculate the running of the three coupling constants in cosmological, topologically massive 3d gravity. We find that \nu, the dimensionless coefficient of the Chern-Simons term, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on \nu, and for any positive \nu there exist both a trivial and a nontrivial fixed point., Comment: 44 pages, 16 figures

It is commonly asserted that there is a \hat G\times G centreless Kac-Moody extension of the manifest G\times G global symmetry of the two-dimensional principal chiral model (PCM) for the group manifold G. Here, we show that the symmetry is in fact larger, namely \hat G\times \hat G, the full centreless Kac-Moody extension of the entire manifest G\times G global symmetry. Extending previous results in the literature, we also obtain an explicit realisation of the Virasoro-like symmetry of the PCM, generated by K_n=L_{n+1} - L_{n-1} for both positive and negative n. We show that these generators obey Sugarawara-type commutation relations with the two commuting copies of the Kac-Moody algebra \hat G., Comment: Reference added; discussion of earlier work extended

We find the general fully non-linear solution of topologically massive supergravity admitting a Killing spinor. It is of plane-wave type, with a null Killing vector field. Conversely, we show that all solutions with a null Killing vector are supersymmetric for one or the other choice of sign for the Chern-Simons coupling constant \mu. If \mu does not take the critical value \mu=\pm 1, these solutions are asymptotically regular on a Poincar\'e patch, but do not admit a smooth global compactification with boundary S^1\times\R. In the critical case, the solutions have a logarithmic singularity on the boundary of the Poincar\'e patch. We derive a Nester-Witten identity, which allows us to identify the associated charges, but we conclude that the presence of the Chern-Simons term prevents us from making a statement about their positivity. The Nester-Witten procedure is applied to the BTZ black hole., Comment: Minor corrections

We construct the most general gaugings of the maximal D=6 supergravity. The theory is (2,2) supersymmetric, and possesses an on-shell SO(5,5) duality symmetry which plays a key role in determining its couplings. The field content includes 16 vector fields that carry a chiral spinor representation of the duality group. We utilize the embedding tensor method which determines the appropriate combinations of these vectors that participate in gauging of a suitable subgroup of SO(5,5). The construction also introduces the magnetic duals of the 5 two-form potentials and 16 vector fields., Comment: 34 pages, latex, reference added, typo's corrected and minor improvements made

The reduction of ten-dimensional heterotic supergravity with Yang-Mills symmetry group K is performed on an arbitrary n-dimensional group manifold G. The reduction involves a nonvanishing 3-form flux, and the Lie algebra of G must have traceless structure constants to ensure the consistency of the reduction at the level of the action. A large class of gauged supergravities in d=10-n with (non)compact gaugings is obtained. The resulting models describe half-maximal gauged supergravities coupled to $ (n + {\rm dim} K)$ vector multiplets. We uncover their hidden $SO(n,n+{\rm dim} K)$ duality symmetry, and the $SO(n,n+{\rm dim} K) / SO(n)\times SO(n+{\rm dim} K)$ coset structure that governs the couplings of the scalar fields. We find that the local gauge symmetry of the d-dimensional theory is $K\times G \ltimes R^n$. Differences from the existing gauged supergravities are highlighted. The consistent truncation to pure half-maximal gauged supergravity in any dimension is shown, and the obstacle to performing a chiral truncation of the theory in d=6 dimensions is found. Among the results obtained are the complete diagonalisation of the fermionic kinetic terms, and other reduction formulae that are applicable to group reductions of supergravities in arbitrary dimensions., Comment: 29 pages

We derive the necessary and sufficient conditions for the existence of a Killing spinor in N=(1,0) gauge supergravity in six dimensions coupled to a single tensor multiplet, vector multiplets and hypermultiplets. These are shown to imply most of the field equations and the remaining ones are determined. In this framework, we find a novel 1/8 supersymmetric dyonic string solution with nonvanishing hypermultiplet scalars. The activated scalars parametrize a 4 dimensional submanifold of a quaternionic hyperbolic ball. We employ an identity map between this submanifold and the internal space transverse to the string worldsheet. The internal space forms a 4 dimensional analog of the Gell-Mann-Zwiebach tear-drop which is noncompact with finite volume. While the electric charge carried by the dyonic string is arbitrary, the magnetic charge is fixed in Planckian units, and hence necessarily non-vanishing. The source term needed to balance a delta function type singularity at the origin is determined. The solution is also shown to have 1/4 supersymmetric AdS_3 x S^3 near horizon limit where the radii are proportional to the electric charge., Comment: 28 pages, latex, minor corrections made

We review our recent exact solution to four-dimensional higher spin gauge theory invariant under a higher spin extension of SO(3,1) and we comment on its cosmological interpretation. We find an effective Einstein-scalar field theory that admits this solution, and we highlight the significance of the Einstein frame and what we call higher spin frame in the cosmological interpretation of the solution. We also compare the properties of the solution with those based on an Einstein-scalar system that arises in a consistent truncation of gauged N=8,D=4 supergravity., Comment: 12 pages, Proceedings of the 4th International Symposium "Quantum Theory and Symmetries" (QTS-4), 15-21 August 2005, Varna, Bulgaria. v2: clarifying remarks and references added

We show that the half-maximal SU(2) gauged supergravity with topological mass term admits coupling of an arbitrary number of n vector multiplets. The chiral circle reduction of the ungauged theory in the dual 2-form formulation gives N=(1,0) supergravity in 6D coupled to 3p scalars that parametrize the coset SO(p,3)/SO(p)x SO(3), a dilaton and (p+3) axions with p < n+1. Demanding that R-symmetry gauging survives in 6D is shown to put severe restrictions on the 7D model, in particular requiring noncompact gaugings. We find that the SO(2,2) and SO(3,1) gauged 7D supergravities give a U(1)_R, and the SO(2,1) gauged 7D supergravity gives an Sp(1)_R gauged chiral 6D supergravities coupled to certain matter multiplets. In the 6D models obtained, with or without gauging, we show that the scalar fields of the matter sector parametrize the coset SO(p+1,4)/SO(p+1)x SO(4), with the (p+3) axions corresponding to its abelian isometries. In the ungauged 6D models, upon dualizing the axions to 4-form potentials, we obtain coupling of p linear multiplets and one special linear multiplet to chiral 6D supergravity., Comment: 41 pages, latex

We give a one-parameter family of exact solutions to four-dimensional higher-spin gauge theory invariant under a deformed higher-spin extension of SO(3,1) and parameterized by a zero-form invariant. All higher-spin gauge fields vanish, while the metric interpolates between two asymptotically AdS4 regions via a dS3-foliated domainwall and two H3-foliated Robertson-Walker spacetimes -- one in the future and one in the past -- with the scalar field playing the role of foliation parameter. All Weyl tensors vanish, including that of spin two. We furthermore discuss methods for constructing solutions, including deformation of solutions to pure AdS gravity, the gauge-function approach, the perturbative treatment of (pseudo-)singular initial data describing isometric or otherwise projected solutions, and zero-form invariants., Comment: 47 pages. v3: global properties of the solution clarified, minor corrections made, discussion and refs revised

We report on an analysis of the Vasiliev construction for minimal bosonic higher-spin master fields with oscillators that are vectors of SO(D-1,2) and doublets of Sp(2,R). We show that, if the original master field equations are supplemented with a strong Sp(2,R) projection of the 0-form while letting the 1-form adjust to the resulting Weyl curvatures, the linearized on-shell constraints exhibit both the proper mass terms and a geometric gauge symmetry with unconstrained, traceful parameters. We also address some of the subtleties related to the strong projection and the prospects for obtaining a finite curvature expansion., Comment: Latex, 39 pages, contribution to the proceedings of the First Solvay Workshop on Higher-Spin Gauge Theory held in Brussels, May 12-14, 2004

The M2-brane is studied from the perspective of superembeddings. We review the derivation of the M2-brane dynamics and the supergravity constraints from the standard superembedding constraint and we discuss explicitly the induced d=3, N=8 superconformal geometry on the worldvolume. We show that the gauged supermembrane, for a target space with a U(1) isometry, is the standard D2-brane in a type IIA supergravity background. In particular, the D2-brane action, complete with the Dirac-Born-Infeld term, arises from the gauged Wess-Zumino worldvolume 4-form via the brane action principle. The discussion is extended to the massive D2-brane considered as a gauged supermembrane in a massive D=11 superspace background. Type IIA supergeometry is derived using Kaluza-Klein techniques in superspace., Comment: Latex, 46 pages, clarifying remarks and references added

In this paper we first give a simple parametrization of the scalar coset manifold of the only known anomaly free chiral gauged supergravity in six dimensions in the absence of linear multiplets, namely gauged minimal supergravity coupled to a tensor multiplet, E_6 x E_7 x U(1)_R Yang-Mills multiplets and suitable number of hypermultiplets. We then construct the potential for the scalars and show that it has a unique minimum at the origin. We also construct a new BPS dyonic string solution in which U(1)_R x U(1) gauge fields, in addition to the metric, dilaton and the 2-form potential, assume nontrivial configurations in any U(1)_R gauged 6D minimal supergravity coupled to a tensor multiplet with gauge symmetry G\supseteq U(1). The solution preserves 1/4 of the 6D supersymmetries and can be trivially embedded in the anomaly free model, in which case the U(1) activated in our solution resides in E_7., Comment: 18pp, v.2 minor corrections made, typos corrected; v.3 references and remarks added, appendix corrected

We examine spherical p-branes in AdS_m x S^n, that wrap an S^p in either AdS_m (p=m-2) or S^n (p=n-2). We first construct a two-spin giant solution expanding in S^n and has spins both in AdS_m and S^n. For (m,n)={(5,5),(4,7),(7,4)}, it is 1/2 supersymmetric, and it reduces to the single-spin giant graviton when the AdS spin vanishes. We study some of its basic properties such as instantons, non-commutativity, zero-modes, and the perturbative spectrum. All vibration modes have real and positive frequencies determined uniquely by the spacetime curvature, and evenly spaced. We next consider the (0+1)-dimensional sigma-models obtained by keeping generally time-dependent transverse coordinates, describing warped product of a breathing-mode and a point-particle on S^n or AdS_m x S^1. The BPS bounds show that the only spherical supersymmetric solutions are the single and the two-spin giants. Moreover, we integrate the sigma-model and separate the canonical variables. We quantize exactly the point-particle part of the motion, which in local coordinates gives Poschl-Teller type potentials, and calculate its contribution to the anomalous dimension., Comment: 45 pages, v3: Supersymmetry of the two-spin solution corrected from 1/4 to 1/2. Sections 2.6 and 3.6 improved. A reference and comments added

We find a new family of supersymmetric vacuum solutions in the six-dimensional chiral gauged N=(1,0) supergravity theory. They are generically of the form AdS_3 x S^3, where the 3-sphere is squashed homogeneously along its Hopf fibres. The squashing is freely adjustable, corresponding to changing the 3-form charge, and the solution is supersymmetric for all squashings. In a limit where the length of the Hopf fibres goes to zero, one recovers, after a compensating rescaling of the fibre coordinate, a solution that is locally the same as the well-known (Minkowski)_4 x S^2 vacuum of this theory. It can now be viewed as a fine tuning of the new more general family. The traditional "Cosmological Constant Problem" is replaced in this theory by the problem of why the four-dimensional (Minkowski)_4 x S^2 vacuum should be selected over other members of the equally supersymmetric AdS_3 x S^3 family. We also obtain a family of dyonic string solutions in the gauged N=(1,0) theory, whose near-horizon limits approach the AdS_3 times squashed S^3 solutions., Comment: Latex, 17 pages; Section 4 improved

N=(1,0) supergravity in six dimensions admits AdS_3\times S^3 as a vacuum solution. We extend our recent results presented in hep-th/0212323, by obtaining the complete N=4 Yang-Mills-Chern-Simons supergravity in D=3, up to quartic fermion terms, by S^3 group manifold reduction of the six dimensional theory. The SU(2) gauge fields have Yang-Mills kinetic terms as well as topological Chern-Simons mass terms. There is in addition a triplet of matter vectors. After diagonalisation, these fields describe two triplets of topologically-massive vector fields of opposite helicities. The model also contains six scalars, described by a GL(3,R)/SO(3) sigma model. It provides the first example of a three-dimensional gauged supergravity that can obtained by a consistent reduction of string-theory or M-theory and that admits AdS_3 as a vacuum solution. There are unusual features in the reduction from six-dimensional supergravity, owing to the self-duality condition on the 3-form field. The structure of the full equations of motion in N=(1,0) supergravity in D=6 is also elucidated, and the role of the self-dual field strength as torsion is exhibited., Comment: Latex, 22 pages, hep-th number corrected

The correspondences proposed previously between higher spin gauge theories and free singleton field theories were recently extended into a more complete picture by Klebanov and Polyakov in the case of the minimal bosonic theory in D=4 to include the strongly coupled fixed point of the 3d O(N) vector model. Here we propose an N=1 supersymmetric version of this picture. We also elaborate on the role of parity in constraining the bulk interactions, and in distinguishing two minimal bosonic models obtained as two different consistent truncations of the minimal N=1 model that retain the scalar or the pseudo-scalar field. We refer to these models as the Type A and Type B models, respectively, and conjecture that the latter is holographically dual to the 3d Gross-Neveu model. In the case of the Type A model, we show the vanishing of the three-scalar amplitude with regular boundary conditions. This agrees with the O(N) vector model computation of Petkou, thereby providing a non-trivial test of the Klebanov-Polyakov conjecture., Comment: 30pp

We obtain a gauged supergravity theory in three dimensions with eight real supersymmetries by means of a Scherk-Schwarz reduction of pure N=(1,0) supergravity in six dimension on the SU(2) group manifold. The SU(2) Yang-Mills fields in the model propagate, since they have an ordinary kinetic term in addition to Chern-Simons couplings. The other propagating degrees of freedom consist of a dilaton, five scalars which parameterise the coset SL(3,R)/SO(3), three vector fields in the adjoint of SU(2), and twelve spin 1/2 fermions. The model admits an AdS_3 vacuum solution. We also show how a charged black hole solution can be obtained, by performing a dimensional reduction of the rotating self-dual string of six-dimensional (1,0) supergravity., Comment: Latex, 24 pages

Interacting AdS_4 higher spin gauge theories with N \geq 1 supersymmetry so far have been formulated as constrained systems of differential forms living in a twistor extension of 4D spacetime. Here we formulate the minimal N=1 theory in superspace, leaving the internal twistor space intact. Remarkably, the superspace constraints have the same form as those defining the theory in ordinary spacetime. This construction generalizes straightforwardly to higher spin gauge theories N>1 supersymmetry., Comment: 24 pp

We study N=1,2,4 higher spin superalgebras in four dimensions and higher spin gauge theories based on them. We extend the existing minimal N=2,4 theories and find a minimal N=1 theory. Utilizing the basic structure of the minimal N=8 theory, we express the full field equations for the N=1,2,4 theories in a universal form without introducing Kleinian operators. We also use a non-minimal N=4 higher spin algebra tensored with U(3) to describe a higher spin extension of N=4 supergravity coupled to the massless vector multiplets arising in the KK spectrum of 11D supergravity on the N=3 supersymmetric AdS_4 x N^{010} background. The higher spin theory also contains a triplet of vector multiplets which may play a role in the super-Higgs effect in which N=4 is broken down to N=3., Comment: Latex, 36 pages, remarks, footnotes and references added

We treat free large N superconformal field theories as holographic duals of higher spin (HS) gauge theories expanded around AdS spacetime with radius R. The HS gauge theories contain massless and light massive AdS fields. The HS current correlators are written in a crossing symmetric form including only exchange of other HS currents. This and other arguments point to the existence of a consistent truncation to massless HS fields. A survey of massless HS theories with 32 supersymmetries in D=4,5,7 (where the 7D results are new) is given and the corresponding composite operators are discussed. In the case of AdS_4, the cubic couplings of a minimal bosonic massless HS gauge theory are described. We examine high energy/small tension limits giving rise to massless HS fields in the Type IIB string on AdS_5 x S^5 and M theory on AdS_{4/7} x S^{7/4}. We discuss breaking of HS symmetries to the symmetries of ordinary supergravity, and a particularly natural Higgs mechanism in AdS_5 x S^5 and AdS_4 x S^7 where the HS symmetry is broken by finite g_{YM}. In AdS_5 x S^5 it is shown that the supermultiplets of the leading Regge trajectory cross over into the massless HS spectrum. We propose that g_{YM}=0 corresponds to a critical string tension of order 1/R^2 and a finite string coupling of order 1/N. In AdS_7 x S^4 we give a rotating membrane solution coupling to the massless HS currents, and describe these as limits of Wilson surfaces in the A_{N-1}(2,0) SCFT, expandable in terms of operators with anomalous dimensions that are asymptotically small for large spin. The minimal energy configurations have semi-classical energy E=s for all s and the geometry of infinitely stretched strings with energy and spin density concentrated at the endpoints., Comment: 77 pages, latex, minor corrections to eqs 4.26-30, a refined discussion of long strings in Sec 5

The minimal bosonic higher spin gauge theory in four dimensions contains massless particles of spin s=0,2,4,.. that arise in the symmetric product of two spin 0 singletons. It is based on an infinite dimensional extension of the AdS_4 algebra a la Vasiliev. We derive an expansion scheme in which the gravitational gauge fields are treated exactly and the gravitational curvatures and the higher spin gauge fields as weak perturbations. We also give the details of an explicit iteration procedure for obtaining the field equations to arbitrary order in curvatures. In particular, we highlight the structure of all the quadratic terms in the field equations., Comment: Latex, 30 pages, several clarifications and few references added

We construct the minimal bosonic higher spin extension of the 7D AdS algebra SO(6,2), which we call hs(8*). The generators, which have spin s=1,3,5,..., are realized as monomials in Grassmann even spinor oscillators. Irreducibility, in the form of tracelessness, is achieved by modding out an infinite dimensional ideal containing the traces. In this a key role is played by the tree bilinear traces which form an SU(2)_K algebra. We show that gauging of hs(8*) yields a spectrum of physical fields with spin s=0,2,4,...which make up a UIR of hs(8*) isomorphic to the symmetric tensor product of two 6D scalar doubletons. The scalar doubleton is the unique SU(2)_K invariant 6D doubleton. The spin s\geq 2 sector comes from an hs(8*)-valued one-form which also contains the auxiliary gauge fields required for writing the curvature constraints in covariant form. The physical spin s=0 field arises in a separate zero-form in a `quasi-adjoint' representation of hs(8*). This zero-form also contains the spin s\geq 2 Weyl tensors, i.e. the curvatures which are non-vanishing on-shell. We suggest that the hs(8*) gauge theory describes the minimal bosonic, massless truncation of M theory on AdS_7\times S^4 in an unbroken phase where the holographic dual is given by N free (2,0) tensor multiplets for large N., Comment: 23 pages, latex

The AdS_5 superalgebra PSU(2,2|4) has an infinite dimensional extension, which we denote by hs(2,2|4). We show that the gauging of hs(2,2|4) gives rise to a spectrum of physical massless fields which coincides with the symmetric tensor product of two AdS_5 spin-1 doubletons (i.e. the N=4 SYM multiplets living on the boundary of AdS_5). This product decomposes into levels \ell=0,1,2,..,\infty of massless supermultiplets of PSU(2,2|4). In particular, the D=5, N=8 supergravity multiplet arises at level \ell=0. In addition to a master gauge field, we construct a master scalar field containing the s=0,1/2 fields, the anti-symmetric tensor field of the gauged supergravity and its higher spin analogs. We define the linearized constraints and obtain the linearized field equations of the full spectrum, including those of D=5,N=8 gauged supergravity and in particular the self-duality equations for the 2-form potentials of the gauged supergravity (forming a 6-plet of SU(4)), and their higher spin cousins with s=2,3,...,\infty., Comment: 36 pages, latex

We use Grassmann even spinor oscillators to construct a bosonic higher spin extension hs(2,2) of the five-dimensional anti-de Sitter algebra SU(2,2), and show that the gauging of hs(2,2) gives rise to a spectrum S of physical massless fields with spin s=0,2,4,... that is a UIR of hs(2,2). In addition to a master gauge field which contains the massless s=2,4,.. fields, we construct a scalar master field containing the massless s=0 field, the generalized Weyl tensors and their derivatives. We give the appropriate linearized constraint on this master scalar field, which together with a linearized curvature constraint produces the correct linearized field equations. A crucial step in the construction of the theory is the identification of a central generator K which is eliminated by means of a coset construction. Its charge vanishes in the spectrum S, which is the symmetric product of two spin zero doubletons. We expect our results to pave the way for constructing an interacting theory whose curvature expansion is dual to a CFT based on higher spin currents formed out of free doubletons in the large N limit. Thus, extending a recent proposal of Sundborg (hep-th/0103247), we conjecture that the hs(2,2) gauge theory describes a truncation of the bosonic massless sector of tensionless Type IIB string theory on AdS_5 x S^5 for large N. This implies AdS/CFT correspondence in a parameter regime where both boundary and bulk theories are perturbative., Comment: 31 pages, latex

We examine the curvature expansion of a the field equations of a four-dimensional higher spin gauge theory extension of anti-de Sitter gravity. The theory contains massless particles of spin 0,2,4,... that arise in the symmetric product of two spin 0 singletons. We cast the curvature expansion into manifestly covariant form and elucidate the structure of the equations and observe a significant simplification., Comment: Contribution to the proceedings of the Gursey Memorial Conference II `M-theory and dualities', Istanbul, June 2000; 12 pages, Latex; typos corrected, reference added

We examine the boundary behaviour of the gauged N=(2,0) supergravity in D=3 coupled to an arbitrary number of scalar supermultiplets which parametrize a Kahler manifold. In addition to the gravitational coupling constant, the model depends on two parameters, namely the cosmological constant and the size of the Kahler manifold. It is shown that regular and irregular boundary conditions can be imposed on the matter fields depending on the size of the sigma model manifold. It is also shown that the super AdS transformations in the bulk produce the transformations of the N=(2,0) conformal supergravity and scalar multiplets on the boundary, containing fields with nonvanishing Weyl weights determined by the ratio of the sigma model and the gravitational coupling constants. Various types of (2,0) superconformal multiplets are found on the boundary and in one case the superconformal symmetry is shown to be realized in an unconventional way., Comment: 28 pages, latex, references added

We study codimension one branes, i.e. p-branes in (p+2)-dimensions, in the superembedding approach for the cases where the worldvolume superspace is embedded in a minimal target superspace with half supersymmetry breaking. This singles out the cases p=1,2,3,5,9. For p=3,5,9 the superembedding geometry naturally involves a fundamental super 2-form potential on the worldvolume whose generalised field strength obeys a constraint deducible from considering an open supermembrane ending on the p-brane. This constraint, together with the embedding constraint, puts the system on-shell for p=5 but overconstrains the 9-brane in D=11 such that the Goldstone superfield is frozen. For p=3 these two constraints give rise to an off-shell linear multiplet on the worldvolume. An alternative formulation of this case is given in which the linear multiplet is dualised to an off-shell scalar multiplet. Actions are constructed for both cases and are shown to give equivalent equations of motion. After gauge fixing a local Sp(1) symmetry associated with shifts in the Sp(1)_R Goldstone modes, we find that the auxiliary fields in the scalar multiplet parametrise a two-sphere. For completeness we also discuss briefly the cases p=1,2 where the equations of motion (for off-shell multiplets) are obtained from an action principle., Comment: 38 pages, latex, cover page corrected

We couple n copies of N=(2,0) scalar multiplets to a gauged N=(2,0) supergravity in 2+1 dimensions which admits AdS_3 as a vacuum. The scalar fields are charged under the gauged R-symmetry group U(1) and parametrize certain Kahler manifolds with compact or non-compact isometries. The radii of these manifolds are quantized in the compact case, but arbitrary otherwise. In the compact case, we find half-supersymmetry preserving and asymptotically Minkowskian black string solutions. For a particular value of the scalar manifold radius, the solution coincides with that of Horne and Horowitz found in the context of a string theory in 2+1 dimensions. In the non-compact case, we find half-supersymmetry preserving and asymptotically AdS_3 string solutions which have naked singularities. We also obtain two distinct AdS_3 supergravities coupled to n copies of N=(1,0) scalar multiplets either by the truncation of the (2,0) model or by a direct construction., Comment: 20 pages, latex, typos corrected in Sec. 4

We review the basic structure of the higher spin extension of D=4, N=8 AdS supergravity. The theory is obtained by gauging the higher spin superalgebra shs^E(8|4) by a procedure pioneered by Vasiliev. The algebra shs^E(8|4) is a subalgebra of the enveloping algebra of OSp(8|4). The physical states of the theory are in one to one correspondence with the symmetric product of two OSp(8|4) singletons. This singleton theory, which may be viewed in a certain limit as the supermembrane theory on AdS_4 x S^7, is expected to describe the dynamics of the higher spin theory. Thus, the higher spin N=8 supergravity on AdS_4 is conjectured to describe the field theory limit of M-theory on AdS_4 x S^7., Comment: 28 pages, latex, uses sprocl.sty, contribution to the John Hopkins Workshop, August 1998, Chalmers, Sweden

The kappa symmetry of an open M2-brane ending on an M5-brane requires geometrical constraints on the embedding of the system in target superspace. These constraints lead to the M5-brane equations of motion, which we review both in superspace and in component (i.e. in Green-Schwarz) formalism. We also describe the embedding of the chiral M5-brane theory in a non-chiral theory where the equations of motion follow from an action that involves a non-chiral 2-form potential, upon the imposition of a non-linear self-duality condition. In this formulation, we find a simplified form of the second order field equation for the worldvolume 2-form potential, and we derive the nonlinear holomorphicity condition on the partition function of the chiral M5-brane., Comment: 21 pages, latex, uses sprocl.sty, contribution to the Trieste Conference on Superfivebranes and Physics in 5+1 Dimensions, 1-3 April, 1998, Trieste, Italy

Nonlinear sigma models arise in supergravity theories with or without matter couplings in various dimensions and they are important in understanding the duality symmetries of M-theory. With this motivation in mind, we review the salient features of gauged and ungauged nonlinear sigma models with or without Wess-Zumino terms for general target spaces in a minimal as well as lifted formulation. Relevant to the question of finding interesting vacua of gauged supergravity theories is the highly constrained potential which arises naturally in these theories. Motivated by this fact, we derive a general and simple formula for a gauge invariant potential of this kind., Comment: 24 pages, latex, uses sprocl.sty, contribution to the R. Arnowitt Fest: A Symposium on Supersymmetry and Gravitation, College Station, TX, 5-7 April 1998

The superembedding approach to $p$-branes is used to study a class of $p$-branes which have linear multiplets on the worldvolume. We refer to these branes as L-branes. Although linear multiplets are related to scalar multiplets (with 4 or 8 supersymmetries) by dualising one of the scalars of the latter to a $p$-form field strength, in many geometrical situations it is the linear multiplet version which arises naturally. Furthermore, in the case of 8 supersymmetries, the linear multiplet is off-shell in contrast to the scalar multiplet. The dynamics of the L-branes are obtained by using a systematic procedure for constructing the Green-Schwarz action from the superembedding formalism. This action has a Dirac-Born-Infeld type structure for the $p$-form. In addition, a set of equations of motion is postulated directly in superspace, and is shown to agree with the Green-Schwarz equations of motion., Comment: revised version, minor changes, references added, 22 pages, no figures, LaTeX

We give a brief history of the passage from strings to branes and we review some aspects of the following topics in M-theory: (a) an extended brane scan, (b) superembedding approach to the dynamics of superbranes and (c) supermembranes in anti de Sitter space, singletons and massless higher spin field theories., Comment: 51 pages, latex, 2 figure files, uses sprocl.sty, contribution to the Abdus Salam Memorial Meeting, 19-22 Nov 1997, Trieste, Italy, a paragraph with new references added

We consider the (1,0) supersymmetric Yang-Mills multiplet coupled to a self-dual tensor multiplet in six dimensions. It is shown that the counterterm required to cancel the one-loop gauge anomaly modifies the classical equations of motion previously obtained by Bergshoeff, Sezgin and Sokatchev (BSS). We discuss the supermultiplet structure of the anomalies exhibited in the resulting equations of motion. The anomaly corrected field equations agree with the global limit, recently obtained by Duff, Liu, Lu and Pope, of a matter coupled supergravity theory in six dimensions. We also obtain the dual formulation of the BSS model in which the tensor multiplet is free while the field equations of the Yang-Mills multiplet contain the fields of the tensor multiplet at the classical level., Comment: 14 pages, latex