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We show that vector solitons can be stable in nonlinear fractional Schrodinger equations with one-dimensional parity-time-symmetric optical lattices. The families of vector solitons with two propagation constants that are present in the different gaps are investigated. It is found that the Levy index cannot change the phase transition point, but it will influence the solitons existence and stability. The effective widths of the two vector soliton components shrink as the Levy index decreases. Some unique soliton propagation properties are found, and soliton propagation simulations are performed to authenticate the results of the stability analyses.

We present analytical results for massless correlators of two vector, tensor, and scalar composite vertices with the Bjorken fractions x and y of order $$ {\alpha}_s^2 $$ α s 2 β0 of QCD. The structure of these correlators ΠV,T,S(x, y; p2) and properties of its main elements are discussed in detail. Special attention is paid to verifying the results and comparing them with known particular cases. We apply the correlators to evaluate radiative corrections to the distribution amplitudes of light mesons within the QCD sum rules.

Using exceptional field theory we construct supersymmetric warped AdS$_7$ vacua of massive IIA and AdS$_6$ vacua of IIB, as well as their consistent truncations including vector multiplets. We show there are no consistent truncations of massive IIA supergravity around its supersymmetric AdS$_7$ vacua with vector multiplets when the Roman's mass is non-vanishing. For AdS$_6$ vacua of IIB supergravity, we find that in addition to the consistent truncation to pure $\mathrm{F}(4)$ gauged SUGRA, the only other half-maximal truncations that are consistent result in $\mathrm{F}(4)$ gauged SUGRA coupled to one or two Abelian vector multiplets, to three non-Abelian vector multiplets, leading to an $\mathrm{ISO}(3)$ gauged SUGRA, or to three non-Abelian plus one Abelian vector multiplet, leading to an $\mathrm{ISO}(3) \times \mathrm{U}(1)$ gauged SUGRA. These consistent truncations with vector multiplets exist when the two holomorphic functions that define the AdS$_6$ vacua satisfy certain differential conditions which we derive. We use these to deduce that no globally regular AdS$_6$ solutions admit a consistent truncation to $\mathrm{F}(4)$ gauged SUGRA with two vector multiplets, and show that the Abelian T-dual of the Brandhuber-Oz vacuum allows a consistent truncation to $\mathrm{F}(4)$ gauged SUGRA with a single vector multiplet., 58 pages plus appendices

In this work, we present an explicit form of the Luescher equation and consider the construction of the operators in different irreducible representations for the case of scattering of two vector particles. The formalism is applied to scalar QED in the Higgs Phase, where the $U(1)$ gauge boson acquires mass., Update to match published version

In this work we present an extension of the L\"uscher formalism to include the interaction of particles with spin, focusing on the scattering of two vector particles. The derived formalism will be applied to Scalar QED in the Higgs Phase, where the U(1) gauge boson acquires mass., Comment: Lattice 2017 proceeding contribution

We study maximally supersymmetric Anti-de Sitter backgrounds in consistent N=2 truncations of type IIB supergravity compactified on the Sasaki-Einstein manifold $T^{1,1}$. In particular, we focus on truncations that contain fields coming from the nontrivial second and third cohomology forms on $T^{1,1}$. These give rise to N=2 supergravity coupled to two vector- and two hypermultiplets (Betti-vector truncation) or one vector- and three hypermultiplets (Betti-hyper truncation), respectively. We find that both truncations admit AdS$_5$ backgrounds with the gauge group always being broken but containing at least an $U(1)_R$ factor. Moreover, in both cases we show that the moduli space of AdS vacua is nontrivial and of maximal dimension. Finally, we explicitly compute the metrics on these moduli spaces., 20 pages; v2: updated references; v3: 21 pages, as published in JHEP

A linear map between two vector spaces has a very important characteristic: a determinant. In modern theory two generalizations of linear maps are intensively used: to linear complexes (the nilpotent chains of linear maps) and to non-linear mappings. Accordingly, determinant of a linear map has two generalizations: to determinants of complexes and to resultants. These quantities are in fact related: resultant of a non-linear map is determinant of the corresponding Koszul complex. We give an elementary introduction into these notions and interrelations, which will definitely play a role in the future development of theoretical physics.

In this work we study the cosmological perturbations in massive bigravity in the presence of non-minimal derivative couplings. For this purpose we consider a specific subclass of Horndeski scalar-tensor interactions that live on the unique composite effective metric. For the viability of the model both metrics have to be dynamical. Nevertheless, the number of allowed kinetic terms is crucial. We adapt to the restriction of having one single kinetic term. After deriving the full set of equations of motion for flat Friedmann-Lemaitre-Robertson-Walker background, we study linear perturbations on top of it. We show explicitly that only four tensor, two vector and two scalar degrees of freedom propagate, one of which being the Horndeski scalar, while the Boulware-Deser ghost can be integrated out., 17 pages, no figure; v2, discussion on the BD ghost extended in Sec.2, references added, matching the published version

Matrix elements, Ag,h(k) (k = 1-6), which describe a general Euler angle transformation of coordinates to which tesseral spherical tensor operators, k,q, are referred have been calculated and extended to include matrix elements for odd k. The matrix elements have been incorporated into a general axis-transformation computer program which relates to parameter sets in any one of the more commonly used tesseral forms, namely, conventional Stevens, normalized Stevens (Racah normalization) and normalized spherical tensor (Koster and Statz normalization) operators. Tables of decomposition functions of tesseral spherical tensor operators, k,q(B,J) (J = S,I), are extended to detail decompositions for terms of dimension BJ7 and, implicitly, for decomposition of any two vector operators k,q(V,W) to experimentally usable single vector forms where VkVWkW (one of kV, kW unity) is the dimension of a general term in the decomposition. Tables detailing the symmetry-allowed terms under the 11 Laue (site) crystal classes are also extended to include tesseral tensorial sets up to rank 8, thus including the new terms. The use of these functions to describe electron paramagnetic resonance studies of high-spin nuclear Zeeman interactions is discussed.

We investigate the evolution of cosmological perturbations during de Sitter inflation in the Einstein-Chern-Simons-Weyl gravity. Primordial massive gravitational waves are composed of one scalar, two vector and four tensor circularly polarized modes. We show that the vector power spectrum decays quickly like a transversely massive vector in the superhorizon limit $z\to 0$. In this limit, the power spectrum coming from massive tensor modes decays quickly, leading to the conventional tensor power spectrum. Also, we find that in the limit of $m^2 \to 0$ (keeping the Weyl-squared term only), the vector and tensor power spectra disappear. It implies that their power spectra are not gravitationally produced because they (vector and tensor) are decoupled from the expanding de Sitter background, as a result of conformal invariance., Comment: 1+24 pages, no figure, version accepted for publication in JCAP

We find an infinite class of non-supersymmetric multi-center solutions to the STU model in five-dimensional ungauged supergravity coupled to two vector multiplets. The solutions are obtained by solving a system of linear equations on a class of Ricci-scalar-flat K\"ahler manifolds studied by LeBrun. After imposing an additional U(1) isometry in the base, we solve the axisymmetric $SU(\infty)$ Toda equation and obtain explicit supergravity solutions containing arbitrary numbers of 2-cycles with cohomological fluxes of all three flavors. This improves upon a previous result where only two of the three fluxes were topologically non-trivial. Imposing regularity and absence of closed timelike curves, we obtain "bubble equations" highly reminiscent of those known in the supersymmetric case. Thus we extend much of the analysis done for BPS bubbling solutions to this new family of non-supersymmetric bubbling solutions., Comment: 51 pages, 8 figures, substantial changes made to improve analysis of orbifold groups in sections 4, 5

In N = 2 Poincare supersymmetry in four space-time dimensions, there exist off-shell supermultiplets with intrinsic central charge, including the important examples of the Fayet-Sohnius hypermultiplet, the linear and the nonlinear vector-tensor (VT) multiplets. One can also define similar supermultiplets in the context of N = 2 anti-de Sitter (AdS) supersymmetry, although the origin of the central charge becomes somewhat obscure. In this paper we develop a general setting for N = 2 AdS supersymmetric theories with central charge. We formulate a supersymmetric action principle in N = 2 AdS superspace and then reformulate it in terms of N = 1 superfields. We prove that N = 2 AdS supersymmetry does not allow existence of a linear VT multiplet. For the nonlinear VT multiplet, we derive consistent superfield constraints in the presence of any number of N = 2 Yang-Mills vector multiplets, give the supersymmetric action and elaborate on the N = 1 superfield and component descriptions of the theory. Our description of the nonlinear VT multiplet in AdS is then lifted to N = 2 supergravity. Moreover, we derive consistent superfield constraints and Lagrangian that describe the linear VT multiplet in N = 2 supergravity in the presence of two vector multiplets, one of which gauges the central charge. These supergravity constructions thus provide the first superspace formulation for the component results derived in arXiv:hep-th/9710212. We also construct higher-derivative couplings of the VT multiplet to any number of N = 2 tensor multiplets., LaTeX, 36 pages. V2: References added, section 6 extended. V3: Typos corrected. Published version: Typos corrected, references updated

The Raychaudhuri equation has seen extensive use in general relativity, most notably in the development of various singularity theorems. In this rather technical article we shall generalize the Raychaudhuri equation in several ways. First an improved version of the standard timelike Raychaudhuri equation is developed, where several key terms are lumped together as a divergence. This already has a number of interesting applications, both within the ADM formalism and elsewhere. Second, a spacelike version of the Raychaudhuri equation is briefly discussed. Third, a version of the Raychaudhuri equation is developed that does not depend on the use of normalized congruences. This leads to useful formulae for the "diagonal" part of the Ricci tensor. Fourth, a "two vector" version of the Raychaudhuri equation is developed that uses two congruences to effectively extract "off diagonal" information concerning the Ricci tensor., 8 pages

The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. The Z3-grading of the exceptional Lie algebras provide such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of three-junctions of strings and membranes. Generalizations are also considered., 25 pages, 4 figures, presentation improved, minor corrections

We construct explicit consistent Kaluza-Klein reductions of type IIB supergravity on HK_4 x S^1, where HK_4 is an arbitrary four-dimensional hyper-Kaehler manifold, and on SE5, an arbitrary five-dimensional Sasaki-Einstein manifold. In the former case we obtain the bosonic action of D=5 N=4 (ungauged) supergravity coupled to two vector multiplets. For the SE_5 case we extend a known reduction, which leads to minimal D=5 N=2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the SE_5. We show that the resulting D=5 action is also consistent with N=4 gauged supergravity coupled to two vector multiplets. This theory has a supersymmetric AdS_5 vacuum, which uplifts to the class of supersymmetric AdS_5 x SE_5 solutions, that spontaneously breaks N=4 to N=2, and also a non-supersymmetric AdS_5 vacuum which uplifts to a class of solutions first found by Romans., Comment: 1+34 pages. v2: Minor typos corrected, three references added. Version to be published in JHEP

Introduces a class of spacetimes in which the metric tensor can be expressed covariantly in terms of the Minkowski metric and two vector fields, orthogonal to each other. It is shown that, when certain covariantly defined components of the Einstein tensor vanish ('main equations'), the remaining components satisfy a true conservation law. The author also obtains the conditions under which a solution of the linearized main equations is a solution of the full main equations. Several simple solutions to these equations-among them the Schwarzschild solution-are obtained. It is argued that these extra conditions are not overly restrictive and that physically interesting vacuum solutions may be obtained by the use of the proposed ansatz.

In [4], Braun, He, Ovrut and Pantev proposed a model of string theory (based on the Calabi‐Yau 3‐fold X defined in [3]) whose low energy limit predicts certain properties of the Standard Model of particle Physics. This model depends on two vector bundles that have to be stable. We calculate the ample cone of X, and prove that one of them is stable, and the other one is not.

The clebsch potential approach to fluid lagrangians is developed in order to establish contact with other approaches to fluids. Three variants of the perfect fluid approach are looked at. The first is an explicit linear lagrangian constructed directly from the clebsch potentials, this has fixed equation of state and explicit expression for the pressure but is less general than a perfect fluid. The second is lagrangians more general than that of a perfect fluid which are constructed from higher powers of the comoving vector. The third is lagrangians depending on two vector fields which can represent both density flow and entropy flow., Comment: 16 pages

Modified Volterra lattice admits two vector generalizations. One of them is studied for the first time. The zero curvature representations, B\"acklund transformations, nonlinear superposition principle and the simplest explicit solutions of soliton and breather type are presented for both vector lattices. The relations with some other integrable equations are established., Comment: 17 pages, 4 figures

The gyroscopic invariance implies the representation of the antisymmetric part of the Hermite-symmetric metric by a vector potential. Therefore we introduce the six functions of this antisymmetric part in general as derived by two vector potentials. Then Einstein's variational principle leads to a slight modification of the Einstein-Schrodinger equations, which just encludes Minkowski's form of the energy-momentum tensor for the electromagnetic field and the gluon field.

Several classes of systems of evolution equations with one or two vector unknowns are considered. We investigate also systems with one vector and one scalar unknown. For these classes all equations having the simplest higher symmetry are listed.

A new set of tetrads is introduced within the framework of SU(2) X U(1) Yang-Mills field theories in four dimensional Lorentz curved spacetimes. Each one of these tetrads diagonalizes separately and explicitly each term of the Yang-Mills stress-energy tensor. Therefore, three pairs of planes also known as blades, can be defined, and make up the underlying geometrical structure, at each point. These tetrad vectors are gauge dependent on one hand, and also in their definition, there is an additional inherent freedom in the choice of two vector fields. In order to get rid of the gauge dependence, another set of tetrads is defined, such that the only choice we have to make is for the two vector fields. A particular choice is made for these two vector fields such that they are gauge dependent, but the transformation properties of these tetrads are analogous to those already known for curved spacetimes where only electromagnetic fields are present. This analogy allows to establish group isomorphisms between the local gauge group SU(2), and the tensor product of the groups of local Lorentz tetrad transformations, either on blade one or blade two. These theorems show explicitly that the local internal groups of transformations are isomorphic to local spacetime groups of transformations. As an example of application of these new tetrads, we exhibit three new gauge invariant objects, and using these objects we show how to diagonalize the Yang-Mills stress-energy tensor in a gauge invariant way., Comment: This new version has a new abstract and the introduction has been modified. There is also a new section, applications. This new section has two subsections: Gauge invariants and Diagonalization of the stress-energy tensor. The conclusion section has also been substantially modified. There is a new appendix

We obtain the general solution for nonextremal 3-charge dilatonic rotating black holes in the five dimensional $\mathrm{U}(1{)}^{3}$ gauged $\mathcal{N}=2$ supergravity coupled to two vector multiplets, in the case where the two rotation parameters are set equal. These solutions encompass all the previously-known extremal solutions, and, by setting the three charges equal, the recently-obtained nonextremal solutions of $\mathcal{N}=2$ gauged five dimensional pure supergravity.

We calculate the coefficients of three-point functions of BMN operators with two vector impurities. We find that these coefficients can be obtained from those of the three-point functions of scalar BMN operators by interchanging the coefficient for the symmetric-traceless representation with the coefficient for the singlet. We conclude that the Z_2 symmetry of the pp-wave string theory is not manifest at the level of field theory three-point correlators., 25 pages, 7 figures. v1: A reference and a footnote added; v2: New contributions found, Z_2 symmetry lost in 3-point functions

An action for a massless graviton interacting with a massive tensor field is proposed. The model is based on coupling the metric tensor to an SP(4) gauge theory spontaneously broken to $SL(2,C)$. The symmetry breaking is achieved by using a Higgs multiplet containing a scalar field and a vector field related by a constraint. We show that in the non-unitary gauge and for the Fierz-Pauli form of the mass term, the six degrees of freedom of the massive tensor are identified with two tensor helicities, two vector helicities of the Goldstone vector, and two scalars present in the Goldstone multiplet. The propagators of this system are well behaved, in contrast to the system consisting of two tensors., Comment: Minor corrections to counting degrees of freedom. References added

In this paper, we discuss some specific features of symmetries of integrable systems which can be used to contruct the Fokas-Gel'fand formula for the immersion of 2D-soliton surfaces, associated with such systems, in Lie algebras. We establish the sufficient condition for the applicability of this formula. This condition requires the existence of two vector fields which generate a common symmetry of the initial system and its corresponding linear spectral problem. This means that these two fields have to be group-related and we determine an explicit form of this relation. It provides a criterion for the selection of symmetries suitable for the use of the Fokas-Gel'fand formula. We include some examples illustrating its application., 17 pages

The implications of conformal invariance, as relevant in quantum field theories at a renormalisation group fixed point, are analysed with particular reference to results for correlation functions involving conserved currents and the energy momentum tensor. Ward identities resulting from conformal invariance are discussed. Explicit expressions for two and three point functions, which are essentially determined by conformal invariance, are obtained. As special cases we consider the three point functions for two vector and an axial current in four dimensions, which realises the usual anomaly simply and unambiguously, and also for the energy momentum tensor in general dimension $d$. The latter is shown to have two linearly independent forms in which the Ward identities are realised trivially, except if $d = 4$, when the two forms become degenerate. This is necessary in order to accommodate the two independent forms present in the trace of the energy momentum tensor on curved space backgrounds for conformal field theories in four dimensions. The coefficients of the two trace anomaly terms are related to the three parameters describing the general energy momentum tensor three point function. The connections with gravitational effective actions depending on a background metric are described. A particular form due to Riegert is shown to be unacceptable. Conformally invariant expressions for the effective action in four dimensions are obtained using the Green function for a differential operator which has simple properties under local rescalings of the metric., Comment: 44 pages uses harvmac, version to be published in Nuclear Physics, some additions, misprints corrected and extra references

We construct new supersymmetric solutions, including AdS bubbles, in an N=2 truncation of five-dimensional N=8 gauged supergravity. This particular truncation is given by N=2 gauged supergravity coupled to two vector multiples and three incomplete hypermultiplets, and was originally investigated in the context of obtaining regular AdS bubble geometries with multiple active R-charges. We focus on cohomogeneity-one solutions corresponding to objects with two equal angular momenta and up to three independent R-charges. Curiously, we find a new set of zero and negative mass solitons asymptotic to AdS_5/Z_k, for k \ge 3, which are everywhere regular without closed timelike curves., Comment: Latex 3 times, 42 pages

Already known results with respect to the existence of a vector potential for the Maxwell field tensor and a tensor potential for Weyl's conformal curvature tensor in four-dimensional spacetimes are generalized. It is shown that there exists a spinor potential of type (n−1,1) for any totally symmetric spinor field of rankn. From this theorem we deduce a series of corollaries, for example, that every antisymmetric tensor of second rank admits a linear representation in terms of the first derivatives of two vector fields. Further, some investigations are made on the existence of potentials for arbitrary symmetric spinors of type (n, m).

A boson representation of the Hamiltonian is introduced to describe collective motions in nuclei. Two interacting vector bosons differing in their 'pseudospin' projections are used. The non-compact symplectic group Sp(12, R) is the group of dynamical symmetry for the Hamiltonian. If the Hamiltonian satisfies the restriction of preservation of the number of bosons, then in the basis of Sp(12, R) its matrix is block-diagonal with respect to the maximal compact subgroup of Sp(12, R), namely the group U(6). The U(6) structure of the number-preserving Hamiltonian is investigated. The two-boson interaction is expressed in terms of the second-order Casimir operators of the various chains of subgroups of U(6).

The interaction between nucleon and antinucleon has been treated from a bosonic viewpoint where also the short-range part is described by the exchange of vector bosons (introduction of a suitable form factor). The energy levels of the bound- and resonance states are explicitly calculated whereby the various bosonic decay processes (up to two vector bosons) are included. In these calculations the coupling constants are taken from the nucleon-nucleon problem whereas slight variations of the form factors were considered. The results (in particular the number of the bound states exhibit some similarities with experimental facts.