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We give a prescription for N=1 supersymmetrization of any (four-dimensional) nonlinear electrodynamics theory with a Lagrangian density satisfying a convexity condition that we relate to semi-classical unitarity. We apply it to the one-parameter ModMax extension of Maxwell electrodynamics that preserves both electromagnetic duality and conformal invariance, and its Born-Infeld-like generalization, proving that duality invariance is preserved. We also establish superconformal invariance of the superModMax theory by showing that its coupling to supergravity is super-Weyl invariant. The higher-derivative photino-field interactions that appear in any supersymmetric nonlinear electrodynamics theory are removed by an invertible nonlinear superfield redefinition., 36 pp. v3 includes further minor corrections and clarifications

Relations between the various formulations of nonlinear p-form electrodynamics with conformal-invariant weak-field and strong-field limits are clarified, with a focus on duality invariant (2n-1)-form electrodynamics and chiral 2n-form electrodynamics in Minkowski spacetime of dimension D=4n and D=4n+2, respectively. We exhibit a new family of chiral 2-form electrodynamics in D=6 for which these limits exhaust the possibilities for conformal invariance; the weak-field limit is related by dimensional reduction to the recently discovered ModMax generalisation of Maxwell's equations. For n>1 we show that the chiral `strong-field' 2n-form electrodynamics is related by dimensional reduction to a new Sl(2;R)-duality invariant theory of (2n-1)-form electrodynamics., 46 pp. Minor corrections plus Note Added with additional references in v2

The strong-field limit for the 2-form potential on an M5-brane yields a conformal chiral 2-form electrodynamics in six dimensions, with gauge-invariant self-interactions but no adjustable coupling constant; the stress tensor is that of a null fluid. Lorentz invariance can be made manifest via an interpretation as a tensionless `space-filling M5-brane', or as a truncation of the infra-red dynamics of an M5-brane in AdS7 x S4., Comment: 31 pages. Additional minor corrections and an additional reference in V3

A manifestly Lorentz invariant action is found for the Floreanini-Jackiw chiral boson. The method involves a novel chiral reduction of the phase-space action for a string, and can be adapted to describe chiral bosons on the heterotic string worldsheet. A similar manifestly Lorentz invariant action is found for an entire class of conformal chiral 2k-form electrodynamics in (4k+2) dimensions which includes the Floreanini-Jackiw theory as the k=0$ case., Comment: 5 pp. Further minor corrections to V3 in V5

The linearized equations of `New Massive Gravity' propagate a parity doublet of massive spin-2 modes in 3D Minkowski spacetime, but a different non-linear extension is made possible by `third-way' consistency. There is a `Chern-Simons-like' action, as for other 3D massive gravity models, but the new theory is `exotic': its action is parity odd. This `Exotic Massive Gravity' is the next-to-simplest case in an infinite sequence of third-way consistent 3D gravity theories, the simplest being the `Minimal Massive Gravity' alternative to `Topologically Massive Gravity'., 33 pp. Further minor corrections in v.4

All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld electrodynamics. The strong-field limit is the same as that found by Bialynicki-Birula from Born-Infeld theory but the weak-field limit is a new one-parameter extension of Maxwell electrodynamics, which is interacting but admits exact light-velocity plane-wave solutions of arbitrary polarisation. Small-amplitude waves on a constant uniform electromagnetic background exhibit birefringence, but one polarisation mode remains lightlike., Comment: 5 pages. v2 includes many simplifications and additional references, and additional material on birefringence

It is known that the Einstein gravitational field equations in D > 4 spacetime dimensions have no time-independent non-singular compactification solutions to de Sitter space if the D-dimensional stress tensor satisfies the Strong Energy Condition (SEC). Here we show, by example, that the SEC alone does not exclude time-dependent non-singular compactifications to de Sitter space, in Einstein conformal frame. However, this possibility is excluded by the combined SEC and Dominant Energy Condition (DEC) because the DEC forces a time-evolution towards a singular D-metric., JGR acknowledges financial support from projects 2017-SGR-929, MINECO grant FPA2016-76005-C. PKT is is partially supported by the STFC consolidated grant ST/P000681/1

A given field theory action determines a set of field equations but other actions may yield equivalent field equations; if so they are on-shell equivalent. They may also be off-shell equivalent, being related by the elimination of auxiliary fields or by local field redefinitions, but this is not guaranteed, as we demonstrate by consideration of the linearized limit of 3D massive gravity models. Failure to appreciate this subtlety has led to incorrect conclusions in recent studies of the "Minimal Massive Gravity" model., Comment: 17 pages, published version

We investigate the implications of energy conditions on cosmological compactification solutions of the higher-dimensional Einstein field equations. It is known that the Strong Energy Condition forbids time-independent compactifications to de Sitter space but allows time-dependent compactifications to other (homogeneous and isotropic) expanding universes that undergo a {\it transient} period of acceleration. Here we show that the same assumptions allow compactification to FLRW universes undergoing {late-time} accelerated expansion; the late-time stress tensor is a perfect fluid but with a lower bound on the pressure/energy-density ratio that excludes de Sitter but allows accelerated power-law expansion. The compact space undergoes a decelerating expansion that leads to decompactification, but on an arbitrarily long timescale., 23 pages. New subsections and references added

We describe non-relativistic limits of the 3D Proca and $\sqrt{\rm Proca}$ theories that yield spin-1 Schroedinger equations. Analogous results are found by generalized null reduction of the 4D Maxwell or complex self-dual Maxwell equations. We briefly discuss the extension to spin-2., The work of PKT is partially supported by the STFC consolidated grant ST/P000681/1.

A Schroedinger equation proposed for the GMP gapped spin-2 mode of fractional Quantum Hall states is found from a novel non-relativistic limit, applicable only in 2+1 dimensions, of the massive spin-2 Fierz-Pauli field equations. It is also found from a novel null reduction of the linearized Einstein field equations in 3+1 dimensions, and in this context a uniform distribution of spin-2 particles implies, via a Brinkmann-wave solution of the non-linear Einstein equations, a confining harmonic oscillator potential for the individual particles., Comment: 5 pages. Additional references, with discussion, in v2, plus improved analysis of parity violation

Starting from the classical action for a spin-zero particle in a D-dimensional anti-Sitter (AdS) spacetime, we recover the Breitenlohner-Freedman bound by quantization. For D=4,5,7, and using an Sl(2;K) spinor notation for K=R,C,H, we find a bi-twistor form of the action for which the AdS isometry group is linearly realised, although only for zero mass when D=4,7, in agreement with previous constructions. For zero mass and D=4, the conformal isometry group is linearly realized. We extend these results to the superparticle in the maximally supersymmetric "AdS x S" string/M-theory vacua, showing that quantization yields a 128+128 component supermultiplet. We also extend them to the null string., 5 pages. 5 pp. Version to be published. Includes various minor corrections and additions, and some additional references

The action for a Galilean superstring is found from a non-relativistic limit of the closed Green-Schwarz (GS) superstring; it has zero tension and provides an example of a massless super-Galilean system A Wess-Zumino term leads to a topological central charge in the Galilean supersymmetry algebra, such that unitarity requires a upper bound on the total momentum. This Galilean-invariant bound, which is also implied by the classical phase-space constraints, is saturated by solutions of the superstring equations of motion that half-preserve supersymmetry. We discuss briefly the extension to the Galilean supermembrane., Comment: 23 pages. Slight revision to clarify a few issues. v3 for further clarification and additional reference

The IR limit of a planar static D3-brane in AdS5 x S5 is a tensionless D3-brane at the AdS horizon, with dynamics governed by a strong-field limit of the Dirac-Born-Infeld action analogous to that found from the Born-Infeld action by Bialynicki-Birula. As in that case, the field equations are those of an interacting 4D conformal invariant field theory with an Sl(2;R) electromagnetic duality invariance, but the D3-brane origin makes these properties manifest. We also find an Sl(2;R)-invariant action for these equations., Comment: 24 pages. Contribution to a volume in memory of Peter Freund. V2 includes an additional reference, an expanded discussion of some issues, especially Lorentz invariance, and corrections of minor errors

In the (super)twistor formulation of massless (super)particle mechanics, the mass-shell constraint is replaced by a "spin-shell" constraint from which the spin content can be read off. We extend this formalism to massive (super)particles (with N-extended spacetime supersymmetry) in three and four space-time dimensions, explaining how the spin-shell constraints are related to spin, and we use it to prove equivalence of the massive N=1 and BPS-saturated N=2 superparticle actions. We also find the supertwistor form of the action for "spinning particles" with N-extended worldline supersymmetry, massless in four dimensions and massive in three dimensions, and we show how this simplifies special features of the N=2 case., 41 pages. v2 has many additional references, and more details of "hidden" supersymmetries of massive superparticle actions. New format in v3, which corrects typos and includes alternative massive 4D superparticle action with only first-class constraints

We present a generally covariant and parity-invariant two-frame field ("zwei-dreibein") action for gravity in three space-time dimensions that propagates two massive spin-2 modes, unitarily, and we use Hamiltonian methods to confirm the absence of unphysical degrees of freedom. We show how zwei-dreibein gravity unifies previous "3D massive gravity" models and extends them, in the context of the AdS/CFT correspondence, to allow for a positive central charge consistent with bulk unitarity.

The action for a massless particle in 4D Minkowski space has a worldline time-reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the N-extended superparticle is shown to be anomalous when N is odd, in the supertwistor formalism this is because a CPT-violating worldline-Chern-Simons term is needed to preserve the chiral U(1) gauge invariance. This accords with the fact that no massless N=1 super-Poincar\'e irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when N is even, but it has $2^{N+1}$ states when N/2 is odd (e.g. the N=2 hypermultiplet) in contrast to just $2^N$ when N/2 is even (e.g. the N=4 Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when N/2 is odd., Comment: 23 pp. Typos corrected, references added and Appendix expanded in v.2. Additional sign choices, simplified equations and clarifications included in v.3

We construct a four-dimensional (4D) gauge theory that propagates, unitarily, the five polarization modes of a massive spin-2 particle. These modes are described by a "dual" graviton gauge potential and the Lagrangian is 4th-order in derivatives. As the construction mimics that of 3D "new massive gravity", we call this 4D model (linearized) "new massive dual gravity". We analyse its massless limit, and discuss similarities to the Eddington-Schroedinger model., Comment: 17 pages, v2 : version published in JHEP

The general second-order massive field equations for arbitrary positive integer spin in three spacetime dimensions, and their "self-dual" limit to first-order equations, are shown to be equivalent to gauge-invariant higher-derivative field equations. We recover most known equivalences for spins 1 and 2, and find some new ones. In particular, we find a non-unitary massive 3D gravity theory with a 5th order term obtained by contraction of the Ricci and Cotton tensors; this term is part of an N=2 super-invariant that includes the "extended Chern-Simons" term of 3D electrodynamics. We also find a new unitary 6th order gauge theory for "self-dual" spin 3., Comment: 23 pp. New references, improved spin-3 discussion. Minor additional corrections in v3

Consistency of Einstein's gravitational field equation $G_{\mu\nu} \propto T_{\mu\nu}$ imposes a "conservation condition" on the $T$-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion, and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a "non-geometrical" action: one {\it not} constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D "minimal massive gravity" model, which resolves the "bulk vs. boundary" unitarity problem of topologically massive gravity with anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher-dimensional theories., Comment: Written for the Gravity Research Foundation essay competition 2015, received an honorable mention

For models of gravity coupled to hyperbolic sigma models, such as the metric-scalar sector of IIB supergravity, we show how smooth trajectories in the `augmented target space' connect FLRW cosmologies to non-extremal D-instantons through a cosmological singularity. In particular, we find closed cyclic universes that undergo an endless sequence of big-bang to big-crunch cycles separated by instanton `phases'. We also find `big-bounce' universes in which a collapsing closed universe bounces off its cosmological singularity to become an open expanding universe., Comment: 21 pages, 4 figures. v2: minor changes

A wide class of three-dimensional gravity models can be put into "Chern-Simons-like" form. We perform a Hamiltonian analysis of the general model and then specialise to Einstein-Cartan Gravity, General Massive Gravity, the recently proposed Zwei-Dreibein Gravity and a further parity violating generalisation combining the latter two.

We present an alternative to Topologically Massive Gravity (TMG) with the same "minimal" bulk properties; i.e. a single local degree of freedom that is realized as a massive graviton in linearization about an anti-de Sitter (AdS) vacuum. However, in contrast to TMG, the new "minimal massive gravity" has both a positive energy graviton and positive central charges for the asymptotic AdS-boundary conformal algebra., Comment: 21 pages. v2 includes additional references and an extended discussion of the unusual features of the MMG equation. Typos corrected in v3 and a "note added" concerning matter coupling. More sign corrections in v4 plus additional "note added"

We find the combinations of momentum and domain-wall charges corresponding to BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how the supersymmetry algebra implies their stability. These states form the boundary of the convex cone associated with the Jordan algebra of $4\times 4$ real symmetric matrices, and we explore some implications of the associated geometry. For the Wess-Zumino model we derive the conditions for preservation of 1/4 supersymmetry when one of two parallel domain-walls is rotated and in addition show that this model does not admit any classical configurations with 3/4 supersymmetry. Our analysis also provides information about BPS states of N=1 D=4 anti-de Sitter supersymmetry., Comment: Latex, 27 pages. Various corrections and improvements including an expanded discussion on BPS states in adS

We obtain the M5-M2-MW bound state solutions of 11-dimensional supergravity corresponding to the 1/2 supersymmetric vacua of the M5-brane equations with constant background fields. In the `near-horizon' case the solution interpolates between the $adS_7\times S^4$ Kaluza-Klein vacuum and D=11 Minkowski spacetime via a Domain Wall spacetime. We discuss implications for renormalization group flow of (2,0) D=6 field theories., 8 pp. Latex. Minor corrections made in revised version

We argue that MQCD admits intersecting domain walls that are realized as Cayley calibrations of the MQCD M5-brane. We discuss various dual realizations and comment on how branes can realise domain walls in N=1 supersymmetric theories in D=3., 10 pages. Very minor changes. Version to be published in Phys. Lett. B

We argue that the large $n$ limit of the $n$-particle $SU(1,1|2)$ superconformal Calogero model provides a microscopic description of the extreme Reissner-Nordstr{\"o}m black hole in the near-horizon limit., Comment: Revtex 5pp. Revision includes improved discussion of entropy and includes an additional reference

The dynamics of a (super)particle near the horizon of an extreme Reissner-Nordstrom black hole is shown to be governed by an action that reduces to a (super)conformal mechanics model in the limit of large black hole mass., Comment: 9 pages, Latex. An argument is added why the study of conformal quantum mechanics has potential applications to the quantum mechanics of black holes. Version accepted in PRL

Domain wall and electrovac solutions of gauged N=4 D=4 supergravity, with gauge group SU(2) or SU(2)xSU(2), are interpreted as supersymmetric Kaluza-Klein vacua of N=1 D=10 supergravity. These vacua are shown to be the near-horizon geometries of certain intersecting brane solutions., 13 pages, no figures, Latex. Revised to take into account some earlier work on the subject. A typo in an equation has been corrected

We determine the possible fractions of supersymmetry preserved by two intersecting M-5-branes. These include the fractions 3/32 and 5/32 which have not occurred previously in intersecting brane configurations. Both occur in non-orthogonal pointlike intersections of M-5-branes but 5/32 supersymmetry is possible only for specific fixed angles., Comment: 11 pages, Latex

A manifestly S-dual, and `12 dimensional', IIB superstring action with an $Sl(2;\bR)$ doublet of `Born-Infeld' fields is presented. The M-theory origin of the 12th dimension is the M-2-brane tension, which can be regarded as the flux of a 3-form worldvolume field strength. The latter is required by the fact that the M-2-brane can have a boundary on an M-5-brane., Comment: 10 pp. Phyzxx. Typos corrected. Some points clarified. Some refs. added (Yesterday's revised version wasn't)

We present a manifestly Lorentz invariant, spacetime supersymmetric, and `$\kappa$-invariant' worldvolume action for all type II Dirichlet p-branes, $p\le9$, in a general type II supergravity background, including massive backgrounds in the IIA case. The $p=0,2$ cases are rederived from D=11. The $p=9$ case provides a supersymmetrization of the D=10 Born-Infeld action., Comment: 27pp. Typos corrected. To appear in Nucl. Phys. B

We perform a light-cone gauge quantization of the Ramond closed spinning string in three spacetime dimensions (3D). The spectrum is Lorentz invariant and identical to that of the 3D Green-Schwarz closed superstring with ${\cal N}=2$ space-time supersymmetry, quantized in light-cone gauge., 15 pages. Revised to include discussion of modular invariance

A number of three-dimensional (3D) gravity models, such as 3D conformal gravity, admit "exotic" black hole solutions: the metric is the same as the Banados-Teitelboim-Zanelli metric of 3D Einstein gravity but with reversed roles for mass and angular momentum, and an entropy proportional to the length of the inner horizon instead of the event horizon. Here we show that the Banados-Teitelboim-Zanelli solutions of the exotic 3D Einstein gravity (with parity-odd action but Einstein field equations) are exotic black holes, and we investigate their thermodynamics. The first and second laws of black hole thermodynamics still apply, and the entropy still has a statistical interpretation.

The 2-brane and 4-brane solutions of ten dimensional IIA supergravity have a dual interpretation as Dirichlet-branes, or `D-branes', of type IIA superstring theory and as `M-branes' of an $S^1$-compactified eleven dimensional supermembrane theory, or M-theory. This eleven-dimensional connection is used to determine the ten-dimensional Lorentz covariant worldvolume action for the Dirichlet super 2-brane, and its coupling to background spacetime fields. It is further used to show that the 2-brane can carry the Ramond-Ramond charge of the Dirichlet 0-brane as a topological charge, and an interpretation of the 2-brane as a 0-brane condensate is suggested. Similar results are found for the Dirichlet 4-brane via its interpretation as a double-dimensional reduction of the eleven-dimensional fivebrane. It is suggested that the latter be interpreted as a D-brane of an open eleven-dimensional supermembrane., Comment: Version to appear in Physics Letters B. Incorporates minor revisions to previous revised version. 16 pp

Symmetry is the most powerful concept we have at our disposal in our attempts to understand the order of the natural world in the subatomic realm. Symmetry expresses the fact, or hope, that the laws of nature at the subatomic level are unchanged under some imagined, or perhaps actual, operation, even though this may not be apparent at higher levels. A simple example is mirror symmetry. If you look at yourself in a mirror it is clear that the person looking back at you from the mirror world is not identical to yourself; there is always some imperfection that would allow an acute observer to spot the difference.