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Matching conditions relating the fields at the future of past null infinity with the fields at the past of future null infinity play a central role in the analysis of asymptotic symmetries and conservation laws in asymptotically flat spacetimes. These matching conditions can be derived from initial data given on a Cauchy hypersurface by integrating forward and backward in time the field equations to leading order in an asymptotic expansion, all the way to future and past null infinities. The standard matching conditions considered in the literature are valid only in the case when the expansion near null infinity (which is generically polylogarithmic) has no dominant logarithmic term. This paper is the first in a series in which we derive the matching conditions for a massless scalar field with initial conditions leading to dominant logarithms at null infinity. We prove that these involve the opposite sign with respect to the usual matching conditions. We also analyse the matching of the angle-dependent conserved charges that follow from the asymptotic decay and Lorentz invariance. We show in particular that these are well defined and finite at null infinity even in the presence of leading logarithmic terms provided one uses the correct definitions. The free massless scalar field has the virtue of presenting the polylogarithmic features in a particularly clear setting that shows their inevitability, since there is no subtle gauge fixing issue or nonlinear intrincacies involved in the problem. We also consider the case of higher spacetime dimensions where fractional powers of $r$ (odd spacetime dimensions) or subdominant logarithmic terms (even spacetime dimensions) are present. Mixed matching conditions are then relevant. In subsequent papers, we will extend the analysis to the electromagnetic and the gravitational fields., Comment: 41 pages. No figures

We analyse the asymptotic symmetries of electromagnetism non-minimally coupled to scalar fields, with non-minimal couplings of the Fermi type that occur in extended supergravity models. Our study is carried out at spatial infinity where minimal and non-minimal couplings exhibit very different asymptotic properties: while the former generically cannot be neglected at infinity, the latter can. Electromagnetic non-minimal couplings are in that respect similar to gravitational minimal couplings, which are also asymptotically subdominant. Because the non-minimally interacting model is asymptotic to the free one, its asymptotic symmetries are the same as the ones of the free theory, i.e., described by angle-dependent $u(1)$ gauge transformations. We also analyse the duality symmetry and show that it is broken to its compact subgroup by the asymptotic conditions. Finally, we consider logarithmic gauge transformations and use them to simplify the symmetry algebra., Comment: 27 pages, no figures. References added. Matches published version in JHEP

We construct Carroll-invariant theories with fields propagating outside the Carroll lightcone, i.e., at a speed strictly greater than zero (`Carroll swiftons'). We first consider models in flat Carroll spacetime in general dimensions, where we present scalar and vector Carroll swifton field theories. We then turn to the coupling to gravity and achieve in particular in two dimensions a Carroll invariant scalar swifton by coupling it suitably to Carroll dilaton gravity. Its backreaction on the geometry generates dynamical torsion., Comment: 8pp, v2: added refs. and extended acknowledgments

The asymptotic structure of gravity in $D=6$ spacetime dimensions is described at spatial infinity in the asymptotically flat context through Hamiltonian (ADM) methods. Special focus is given on the BMS supertranslation subgroup. It is known from previous studies that the BMS group contains more supertranslations as one goes from $D=4$ to $D=5$. Indeed, while the supertranslations are described by one single function of the angles in $D=4$, four such functions are neeeded in $D=5$. We consider the case $D=6$ with the aim of determining whether the number of supertranslations keeps increasing with the dimension or remains equal to the number found in $D=5$. We show that even though there is apparent room for more supertranslations, their number remains equal to the $D=5$ value (four): the potentially new supertranslations turn out to define proper gauge transformations corresponding to a redundancy in the description of the system. Critical in the analysis are the boundary conditions chosen to yield a well-defined canonical formalism. Given the computational (but not conceptual) complexity as one increases the dimension, we explicitly discuss the linearized theory and argue that asymptotically, this analysis provides the correct picture. We conclude by considering higher spacetime dimensions where we indicate that the number of physically relevant supertranslations remains equal to four independently of the dimension $\geq 5$., Comment: 24 pages, no figures. Contribution to Stanley Deser memorial volume "Gravity, Strings and Beyond''

We show that the non-linear BMS$_5$ symmetry algebra of asymptotically flat Einstein gravity in five dimensions, as well as the super-BMS$_4$ superalgebra of asymptotically flat supergravity, can be redefined so as to take a direct sum structure. In the new presentation of the (super-)algebra, angle-dependent translations and angle-dependent supersymmetry transformations commute with the (super-)Poincar\'e generators. We also explain in detail the structure and charge-integrability of asymptotic symmetries with symmetry parameters depending on the fields (through the charges themselves), a topic relevant for nonlinear asymptotic symmetry algebras., Comment: 23 pages, no figures

It is shown how the gluing theorem due to Corvino and Shoen can be naturally extended to accommodate supertranslations at spatial infinity. Logarithmic supertranslations play an intersting role in the construction., Comment: To appear in World Scientific volume dedicated to the memory of Lars Brink

The asymptotic symmetry algebra of four-dimensional Einstein gravity in the asymptotically flat context has been shown recently to be the direct sum of the Poincar\'e algebra and of an infinite-dimensional abelian algebra (with central charge) that includes the Bondi-Metzner-Sachs supertranslations. This result, obtained within the Hamiltonian formalism, yields a supertranslation invariant definition of the Lorentz generators (angular momentum and boosts). Definitions of Lorentz generators free from the ``supertranslation ambiguities'' have also been proposed recently at null infinity. We prove the equivalence of the two approaches for redefining the charges., Comment: 6 pages, no figures. Footnote and references added. Matches published version in PRL

We extend the asymptotic symmetries of electromagnetism in order to consistently include angle-dependent $u(1)$ gauge transformations $\epsilon$ that involve terms growing at spatial infinity linearly and logarithmically in $r$, $\epsilon \sim a(\theta, \varphi) r + b(\theta, \varphi) \ln r + c(\theta, \varphi)$. The charges of the logarithmic $u(1)$ transformations are found to be conjugate to those of the $\mathcal O(1)$ transformations (abelian algebra with invertible central term) while those of the $\mathcal O(r)$ transformations are conjugate to those of the subleading $\mathcal O(r^{-1})$ transformations. Because of this structure, one can decouple the angle-dependent $u(1)$ asymptotic symmetry from the Poincar\'e algebra, just as in the case of gravity: the generators of these internal transformations are Lorentz scalars in the redefined algebra. This implies in particular that one can give a definition of the angular momentum which is free from $u(1)$ gauge ambiguities. The change of generators that brings the asymptotic symmetry algebra to a direct sum form involves non linear redefinitions of the charges. Our analysis is Hamiltonian throughout and carried at spatial infinity., Comment: 25 pages, no figures. One note added and minor typos corrected. Matches with published version

We extend the BMS(4) group by adding logarithmic supertranslations. This is done by relaxing the boundary conditions on the metric and its conjugate momentum at spatial infinity in order to allow logarithmic terms of carefully designed form in the asymptotic expansion, while still preserving finiteness of the action. Standard theorems of the Hamiltonian formalism are used to derive the (finite) generators of the logarithmic supertranslations. As the ordinary supertranslations, these depend on a function of the angles. Ordinary and logarithmic supertranslations are then shown to form an abelian subalgebra with non-vanishing central extension. Because of this central term, one can make nonlinear redefinitions of the generators of the algebra so that the pure supertranslations ($\ell >1$ in a spherical harmonic expansion) and the logarithmic supertranslations have vanishing brackets with all the Poincar\'e generators, and, in particular, transform in the trivial representation of the Lorentz group. The symmetry algebra is then the direct sum of the Poincar\'e algebra and the infinite-dimensional abelian algebra formed by the pure supertranslations and the logarithmic supertranslations (with central extension). The pure supertranslations are thus completely decoupled from the standard Poincar\'e algebra in the asymptotic symmetry algebra. This implies in particular that one can provide a definition of the angular momentum which is manifestly free from supertranslation ambiguities. An intermediate redefinition providing a partial decoupling of the pure and logarithmic supertranslations is also given., Comment: 52 pages, no figures, one comment added

We explicitly establish the equivalence between the magnetic Carrollian limit of Einstein gravity defined through the Hamiltonian formalism and the Carrollian theory of gravity defined through a gauging of the Carroll algebra along the lines of standard Poincar\'e (or (A)dS) gaugings., Comment: 24 pages

In this paper, three things are done. First, we study from an algebraic point of view the infinite-dimensional BMS-like extensions of the Carroll algebra relevant to the asymptotic structure of the electric and magnetic Carrollian limits of Einstein gravity. In the course of this study we exhibit by "Carroll-Galileo duality" a new infinite-dimensional BMS-like extension of the Galilean algebra and of its centrally extended Bargmann algebra. Second, we consider the electric Carrollian limit of the pure Einstein theory and indicate that more flexible boundary conditions than the ones that follow from just taking the limit of the Einsteinian boundary conditions are actually consistent. These boundary conditions lead to a bigger asymptotic symmetry algebra that involves spatial supertranslations depending on three functions of the angles (instead of one). Third, we turn to the Carrollian limit of the coupled Einstein-Yang-Mills system. An infinite-dimensional color enhancement of the gauge algebra is found in the electric Carrollian limit of the Yang-Mills field, which allows angle-dependent Yang-Mills transformations at spatial infinity, not available in the Einstein-Yang-Mills case prior to taking the Carrollian electric limit. This enhancement does not occur in the magnetic limit., Comment: 34 pages, no figures

We develop the analysis of the asymptotic properties of gravity in higher spacetime dimensions $D$, with a particular emphasis on the case $D=5$. Our approach deals with spatial infinity and is Hamiltonian throughout. It is shown that the asymptotic symmetry algebra BMS$_5$, which is realized non linearly, contains a four-fold family of angle-dependent supertranslations. The structure of this non-linear algebra is investigated and a presentation in which the Poincar\'e subalgebra is linearly realized is constructed. Invariance of the energy is studied. Concluding comments on higher dimensions $D \geq 6$ are also given., Comment: 56 pages, no figures. References added and minor typo corrected

The final (close to the singularity) dynamical behavior of the metric inside black holes with massive charged scalar or vector hair is analyzed for general anisotropic and inhomogeneous initial conditions. These solutions are relevant to a holographic realization of superconductivity. It is shown that the dynamics falls within the scope of the "cosmological billiard" description and that in both cases, the corresponding hyperbolic billiard region has infinite volume so that the system ultimately settles down to a final Kasner regime. For massive vector hair, the conclusion holds because the longitudinal mode plays the same role as a scalar field. There exists, however, a measure-zero subset of solutions characterized by vanishing longitudinal modes that exhibit a chaotic behavior with an infinite number of BKL oscillations as one goes to the singularity., Comment: Minor misprints corrected

We study asymptotically flat spacetimes in five spacetime dimensions by Hamiltonian methods, focusing on spatial infinity and keeping all asymptotically relevant nonlinearities in the transformation laws and in the charge-generators. Precise boundary conditions that lead to a consistent variational principle are given. We show that the algebra of asymptotic symmetries, which had not been uncovered before, is a nonlinear deformation of the semi-direct product of the Lorentz algebra by an abelian algebra involving four independent (and not just one) arbitrary functions of the angles on the $3$-sphere at infinity, with non trivial central charges. The nonlinearities occur in the Poisson brackets of the boost generators with themselves and with the other generators. They would be invisible in a linearized treatment of infinity., Comment: 5 pages, no figures

We consider Carroll-invariant limits of Lorentz-invariant field theories. We show that just as in the case of electromagnetism, there are two inequivalent limits, one "electric" and the other "magnetic". Each can be obtained from the corresponding Lorentz-invariant theory written in Hamiltonian form through the same "contraction" procedure of taking the ultrarelativistic limit $c \rightarrow 0$ where $c$ is the speed of light, but with two different consistent rescalings of the canonical variables. This procedure can be applied to general Lorentz-invariant theories ($p$-form gauge fields, higher spin free theories etc) and has the advantage of providing explicitly an action principle from which the electrically-contracted or magnetically-contracted dynamics follow (and not just the equations of motion). Even though not manifestly so, this Hamiltonian action principle is shown to be Carroll invariant. In the case of $p$-forms, we construct explicitly an equivalent manifestly Carroll-invariant action principle for each Carroll contraction. While the manifestly covariant variational description of the electric contraction is rather direct, the one for the magnetic contraction is more subtle and involves an additional pure gauge field, whose elimination modifies the Carroll transformations of the fields. We also treat gravity, which constitutes one of the main motivations of our study, and for which we provide the two different contractions in Hamiltonian form., Comment: 29 pages

Super-BMS$_4$ algebras -- also called BMS$_4$ superalgebras -- are graded extensions of the BMS$_4$ algebra. They can be of two different types: they can contain either a finite number or an infinite number of fermionic generators. We show in this letter that, with suitable boundary conditions on the graviton and gravitino fields at spatial infinity, supergravity on asymptotically flat spaces possesses as superalgebra of asymptotic symmetries a (nonlinear) super-BMS$_4$ algebra containing an infinite number of fermionic generators, which we denote SBMS$_4$. These boundary conditions are not only invariant under SBMS$_4$, but also lead to a fully consistent canonical description of the supersymmetries, which have in particular well-defined Hamiltonian generators that close according to the nonlinear SBMS$_4$ algebra. One finds in particular that the graded brackets between the fermionic generators yield all the BMS$_4$ supertranslations, of which they provide therefore "square roots"., Comment: 7 pages, no figures

We investigate the asymptotic structure of the free Rarita-Schwinger theory in four spacetime dimensions at spatial infinity in the Hamiltonian formalism. We impose boundary conditions for the spin-3/2 field that are invariant under an infinite-dimensional (abelian) algebra of non-trivial asymptotic fermionic symmetries. The compatibility of this set of boundary conditions with the invariance of the theory under Lorentz boosts requires the introduction of boundary degrees of freedom in the Hamiltonian action, along the lines of electromagnetism. These boundary degrees of freedom modify the symplectic structure by a surface contribution appearing in addition to the standard bulk piece. The Poincar\'e transformations have then well-defined (integrable, finite) canonical generators. Moreover, improper fermionic gauge symmetries, which are also well-defined canonical transformations, are further enlarged and turn out to be parametrized by two independent angle-dependent spinor functions at infinity, which lead to an infinite-dimensional fermionic algebra endowed with a central charge. We extend next the analysis to the supersymmetric spin-$(1,3/2)$ and spin-$(2,3/2)$ multiplets. First, we present the canonical realization of the super-Poincar\'e algebra on the spin-$(1,3/2)$ multiplet, which is shown to be consistently enhanced by the infinite-dimensional abelian algebra of angle-dependent bosonic and fermionic improper gauge symmetries associated with the electromagnetic and the Rarita-Schwinger fields, respectively. A similar analysis of the spin-$(2,3/2)$ multiplet is then carried out to obtain the canonical realization of the super-Poincar\'e algebra, consistently enhanced by the abelian improper bosonic gauge transformations of the spin-$2$ field (BMS supertranslations) and the abelian improper fermionic gauge transformations of the spin-$3/2$ field., Comment: 33 pages, no figures, minor changes made in the text and some equations simplified, this version matches the one published in JHEP

The asymptotic structure of the Pauli-Fierz theory at spatial infinity is investigated in four spacetime dimensions. Boundary conditions on the massless spin-$2$ field that are invariant under an infinite-dimensional group of non-trivial ``improper'' gauge symmetries are given. The compatibility of these boundary conditions with invariance of the theory under Lorentz boosts is a subtle issue which is investigated in depth and leads to the identification of the improper gauge symmetries with the pure BMS supertranslations. It is also shown how rigid Poincar\'e transformations and improper gauge symmetries of the free Pauli-Fierz theory merge into the full BMS group as one switches on the gravitational coupling. Contrary to the massless spin-$1$ case, where invariance under boosts is implemented differently and where important differences between the free and the interacting cases have been exhibited recently, the free Pauli-Fierz theory and general relativity show very similar behaviours at spatial infinity., Comment: 36 pages

Explicit boundary conditions are given at spatial infinity for four-dimensional supergravity, which provide a realization of the super-BMS algebra of Awada, Gibbons and Shaw. The results are then generalized to the $N$- extended super-BMS algebras., Comment: 12 pages, one reference added, minor style changes

We derive the asymptotic symmetries of the manifestly duality invariant formulation of electromagnetism in Minkoswki space. We show that the action is invariant under two algebras of angle-dependent $u(1)$ transformations, one electric and the other magnetic. As in the standard electric formulation, Lorentz invariance requires the addition of additional boundary degrees of freedom at infinity, found here to be of both electric and magnetic types. A notable feature of this duality symmetric formulation, which we comment upon, is that the on-shell values of the zero modes of the gauge generators are equal to only half of the electric and magnetic fluxes (the other half is brought in by Dirac-string type contributions). Another notable feature is the absence of central extension in the angle-dependent $u(1)^2$-algebra., Comment: 15 pages - minor corrections

The asymptotic dynamics of AdS$_3$ gravity with two asymptotically anti-de Sitter regions is investigated, paying due attention to the zero modes, i.e., holonomies along non-contractible circles and their canonically conjugates. This situation covers the eternal black hole solution. We derive how the holonomies around the non-contractible circles couple the fields on the two different boundaries and show that their canonically conjugate variables, needed for a consistent dynamical description of the holonomies, can be related to Wilson lines joining the boundaries. The action reduces to the sum of four free chiral actions, one for each boundary and each chirality, with additional non-trivial couplings to the zero modes which are explicitly written. While the Gauss decomposition of the $SL(2,\mathbb{R})$ group elements is useful in order to treat hyperbolic holonomies, the Iwasawa decomposition turns out to be more convenient in order to deal with elliptic and parabolic holonomies. The connection with the geometric action is also made explicit. Although our paper deals with the specific example of two asymptotically anti-de Sitter regions, most of our global considerations on holonomies and radial Wilson lines qualitatively apply whenever there are multiple boundaries, independently of the form that the boundary conditions explicitly take there., Comment: 44 pages, 2 figures. v2: minor changes, matches version accepted for publication in JHEP

The (free) graviton admits, in addition to the standard Pauli-Fierz description by means of a rank-two symmetric tensor, a description in which one dualizes the corresponding (2,2)-curvature tensor on one column to get a (D-2,2)-tensor, where D is the spacetime dimension. This tensor derives from a gauge field with mixed Yound symmetry (D-3,1) called the "dual graviton" field. The dual graviton field is related non-locally to the Pauli-Fierz field (even on-shell), in much the same way as a p-form potential and its dual (D-p-2)-form potential are related in the theory of an abelian p-form. Since the Pauli-Fierz field has a Young tableau with two columns (of one box each), one can contemplate a double dual description in which one dualizes on both columns and not just on one. The double dual curvature is now a (D-2,D-2)-tensor and derives from a gauge field with (D-3, D-3) mixed Young symmetry, the "double dual graviton" field. We show, however, that the double dual graviton field is algebraically and locally related to the original Pauli-Fierz field and, so, does not provide a truly new description of the graviton. From this point of view, it plays a very different role from the dual graviton field obtained through a single dualization. We also show that these equations can be obtained from a variational principle in which the variables to be varied in the action are (all) the components of the double-dual field as well as an auxiliary field with (2,1) Young symmetry. By gauge fixing the shift symmetries of this action principle, one recovers the Pauli-Fierz action. Our approach differs from the interesting approach based on parent actions and covers only the free, sourceless theory. Similar results are argued to hold for higher spin gauge fields., Comment: v2: some clarifications and updated references. 13 pages. Submitted for publication in the memorial volume for Peter Freund

A review of our results on the asymptotic structure of gravity at spatial infinity in four spacetime dimensions is given. Finiteness of the action and integrability of the asymptotic Lorentz boost generators are key criteria that we implement through appropriate boundary conditions. These conditions are `twisted parity conditions', expressing that the leading order of the asymptotic fields obey strict parity conditions under the sphere antipodal map up to an improper gauge transformation. The asymptotic symmetries are shown to form the infinite-dimensional BMS group, which has a non trivial action. The charges and their algebra are worked out. The presentation aims at being self-contained and at possessing a pedagogical component., Comment: 31 pages, review article dedicated to Andrei Slavnov on the occasion of his 80th birthday, appendix C added in version 2

We investigate the asymptotic structure of electromagnetism in Minkowski space in even and odd spacetime dimensions $\geq 4$. We focus on $d>4$ since the case $d=4$ has been studied previously at length. We first consider spatial infinity where we provide explicit boundary conditions that admit the known physical solutions and make the formalism well defined (finite symplectic structure and charges). Contrary to the situation found in $d=4$ dimensions, there is no need to impose parity conditions under the antipodal map on the leading order of the fields when $d>4$. There is, however, the same need to modify the standard bulk symplectic form by a boundary term at infinity involving a surface degree of freedom. This step makes the Lorentz boosts act canonically. Because of the absence of parity conditions, the theory is found to be invariant under two independent algebras of angle-dependent $u(1)$ transformations ($d>4$). We then integrate the equations of motion in order to find the behaviour of the fields near null infinity. We exhibit the radiative and Coulomb branches, characterized by different decays and parities. The analysis yields generalized matching conditions between the past of $\mathscr{I}^+$ and the future of $\mathscr{I} ^-$., Comment: 46 pages

Relativistic field theories with a power law decay in $r^{-k}$ at spatial infinity generically possess an infinite number of conserved quantities because of Lorentz invariance. Most of these are not related in any obvious way to symmetry transformations of which they would be the Noether charges. We discuss the issue in the case of a massless scalar field. By going to the dual formulation in terms of a $2$-form (as was done recently in a null infinity analysis), we relate some of the scalar charges to symmetry transformations acting on the $2$-form and on surface degrees of freedom that must be added at spatial infinity. These new degrees of freedom are necessary to get a consistent relativistic description in the dual picture, since boosts would otherwise fail to be canonical transformations. We provide explicit boundary conditions on the $2$-form and its conjugate momentum, which involves parity conditions with a twist, as in the case of electromagnetism and gravity. The symmetry group at spatial infinity is composed of `improper gauge transformations'. It is abelian and infinite-dimensional. We also briefly discuss the realization of the asymptotic symmetries, characterized by a non trivial central extension and point out vacuum degeneracy.

We introduce prepotentials for fermionic higher-spin gauge fields in four spacetime dimensions, generalizing earlier work on bosonic fields. To that end, we first develop tools for handling conformal fermionic higher-spin gauge fields in three dimensions. This is necessary because the prepotentials turn out to be three-dimensional fields that enjoy both "higher-spin diffeomorphism" and "higher-spin Weyl" gauge symmetries. We discuss a number of the key properties of the relevant Cotton tensors. The reformulation of the equations of motion as "twisted self-duality conditions" is then exhibited. We show next how the Hamiltonian constraints can be explicitly solved in terms of appropriate prepotentials and show that the action takes then the same remarkable form for all spins., Comment: 25+6 pages, 1 table, v2: 1 reference added

We present a new set of asymptotic conditions for gravity at spatial infinity that includes gravitational magnetic-type solutions, allows for a non-trivial Hamiltonian action of the complete $BMS_4$ algebra, and leads to a non-divergent behaviour of the Weyl tensor as one approaches null infinity. We then extend the analysis to the coupled Einstein-Maxwell system and obtain as canonically realized asymptotic symmetry algebra a semi-direct sum of the $BMS_4$ algebra with the angle dependent $u(1)$ transformations. The Hamiltonian charge-generator associated with each asymptotic symmetry element is explicitly written. The connection with matching conditions at null infinity is also discussed., Comment: 23 pages

The action of the free $\mathcal{N} = (3,1)$ theory in six spacetime dimensions is explicitly constructed. The variables of the variational principle are prepotentials adapted to the self-duality conditions on the fields. The $(3,1)$ supersymmetry variations are given and the invariance of the action is verified. The action is first-order in time derivatives. It is also Poincar\'e invariant but not manifestly so, just like the Hamiltonian action of more familiar relativistic field theories., Comment: 14 pages + 17 pages of appendices, 1 figure. v2: some typos corrected v3: more typos corrected, matches published version

We analyse the asymptotic symmetries of Maxwell theory at spatial infinity through the Hamiltonian formalism. Precise, consistent boundary conditions are explicitly given and shown to be invariant under asymptotic angle-dependent $u(1)$-gauge transformations. These symmetries generically have non-vanishing charges. The algebra of the canonical generators of this infinite-dimensional symmetry with the Poincar\'e charges is computed. The treatment requires the addition of surface degrees of freedom at infinity and a modification of the standard symplectic form by surface terms. We extend the general formulation of well-defined generators and Hamiltonian vector fields to encompass such boundary modifications of the symplectic structure. Our study covers magnetic monopoles., Comment: 30 pages

New boundary conditions for asymptotically flat spacetimes are given at spatial infinity. These boundary conditions are invariant under the BMS group, which acts non trivially. The boundary conditions fulfill all standard consistency requirements: (i) they make the symplectic form finite; (ii) they contain the Schwarzchild solution, the Kerr solution and their Poincar\'e transforms, (iii) they make the Hamiltonian generators of the asymptotic symmetries integrable and well-defined (finite). The boundary conditions differ from the ones given earlier in the literature in the choice of the parity conditions. It is this different choice of parity conditions that makes the action of the BMS group non trivial. Our approach is purely Hamiltonian and off-shell throughout., Comment: 26 pages

Abelian vector fields non-minimally coupled to uncharged scalar fields arise in many contexts. We investigate here through algebraic methods their consistent deformations ("gaugings"), i.e., the deformations that preserve the number (but not necessarily the form or the algebra) of the gauge symmetries. Infinitesimal consistent deformations are given by the BRST cohomology classes at ghost number zero. We parametrize explicitly these classes in terms of various types of global symmetries and corresponding Noether currents through the characteristic cohomology related to antifields and equations of motion. The analysis applies to all ghost numbers and not just ghost number zero. We also provide a systematic discussion of the linear and quadratic constraints on these parameters that follow from higher-order consistency. Our work is relevant to the gaugings of extended supergravities., Comment: v2: references added, typos corrected, minor changes for clarity

The $(4,0)$ theory in six dimensions is an exotic theory of supergravity that has been argued to emerge as the strong coupling limit of theories having $N=8$ supergravity as their low energy effective theory in five spacetime dimensions. It has maximal supersymmetry and is superconformal. Very little is known about this intriguing theory. While the spectrum of fields occurring in its description has been given and their equations of motion in the absence of interactions have been written down, no action principle has been formulated, even in the free case. We extend here previous analyses by writing explicitly the action of the free $(4,0)$ theory from which the equations of motion derive. The variables of the variational principle are prepotentials adapted to the self-duality properties of the fields. The "exotic gravitini", described by chiral fermionic two-forms, are given special attention. The supersymmetry transformations are written down and the invariance of the action is explicitly proven. Even though the action is not manifestly covariant, the symmetry transformations are shown to close according to the $(4,0)$-extended Poincar\'e supersymmetry algebra. We also discuss exotic supergravity models with fewer supersymmetries. Remarks on dimensional reduction close the paper., Comment: v3: updated references

The variety of consistent "gauging" deformations of supergravity theories in four dimensions depends on the choice of Lagrangian formulation. One important goal is to get the most general deformations without making hidden assumptions. Ignoring supersymmetry we consider in this paper $n_v$ abelian vector potentials in four spacetime dimensions with non-minimal kinetic coupling to $n_s$ uncharged (possibly nonlinear) scalar fields. As in the case of extended supergravities, one model may possess different formulations related by $Sp(2n_v,\mathbb{R})$. The symplectic group mixes its electric and magnetic potentials. The model admits a global duality symmetry subgroup $G$ which acts also on the scalars. We recall first how the general second order Lagrangian, its local deformations and those of its abelian gauge group will depend on the choice of $2n_v$ directions (choice of "Darboux frame"). We start from a general frame defined by the symplectic transformation relating it to a fixed"reference" one. Combinations of symplectic matrix coefficients appear then as constant parameters in the second order Lagrangians. Another gauging method uses an "embedding tensor" that characterizes the realization of the gauge group via the global duality group. It involves additional 2-form gauge fields. A suitable zero charge limit of this realization has abelian gauge group and the "gauging" can be viewed as a consistent deformation of that limit. We show that the two methods applied to the corresponding ungauged models have equivalent local deformations -- and more generally, have isomorphic local BRST cohomology at all ghost numbers. We finally consider manifestly duality invariant first order actions with abelian gauge group. We point out that obstructions to non-abelian deformations of the Yang-Mills type exhibited in a previous work remain present when couplings to scalar fields are included.

We reexamine canonical quantization of the gauged Rarita-Schwinger theory using the extended theory, incorporating a dimension $\frac{1}{2}$ auxiliary spin-$\frac{1}{2}$ field $\Lambda$, in which there is an exact off-shell gauge invariance. In $\Lambda=0$ gauge, which reduces to the original unextended theory, our results agree with those found by Johnson and Sudarshan, and later verified by Velo and Zwanziger, which give a canonical Rarita-Schwinger field Dirac bracket that is singular for small gauge fields. In gauge covariant radiation gauge, the Dirac bracket of the Rarita-Schwinger fields is nonsingular, but does not correspond to a positive semi-definite anticommutator, and the Dirac bracket of the auxiliary fields has a singularity of the same form as found in the unextended theory. These results indicate that gauged Rarita-Schwinger theory is somewhat pathological, and cannot be canonically quantized within a conventional positive semi-definite metric Hilbert space. We leave open the questions of whether consistent quantizations can be achieved by using an indefinite metric Hilbert space, by path integral methods, or by appropriate couplings to conventional dimension $\frac{3}{2}$ spin-$\frac{1}{2}$ fields., Comment: Latex, 17 pages

Through timelike dualities, one can generate exotic versions of $M$-theory with different spacetime signatures. These are the $M^*$-theory with signature $(9,2,-)$, the $M'$-theory, with signature $(6,5,+)$ and the theories with reversed signatures $(1,10, -)$, $(2,9, +)$ and $(5,6, -)$. In $(s,t, \pm)$, $s$ is the number of space directions, $t$ the number of time directions, and $\pm$ refers to the sign of the kinetic term of the $3$ form. The only irreducible pseudo-riemannian manifolds admitting absolute parallelism are, besides Lie groups, the seven-sphere $S^7 \equiv SO(8)/SO(7)$ and its pseudo-riemannian version $S^{3,4} \equiv SO(4,4)/SO(3,4)$. [There is also the complexification $SO(8,\mathbb{C})/SO(7, \mathbb{C})$, but it is of dimension too high for our considerations.] The seven-sphere $S^7\equiv S^{7,0}$ has been found to play an important role in $11$-dimensional supergravity, both through the Freund-Rubin solution and the Englert solution that uses its remarkable parallelizability to turn on non trivial internal fluxes. The spacetime manifold is in both cases $AdS_4 \times S^7$. We show that $S^{3,4}$ enjoys a similar role in $M'$-theory and construct the exotic form $AdS_4 \times S^{3,4}$ of the Englert solution, with non zero internal fluxes turned on. There is no analogous solution in $M^*$-theory., Comment: 18 pages, v2: typos fixed

We build the asymptotic higher-spin charges associated with "improper" gauge transformations for fermionic higher-spin gauge fields on Anti de Sitter backgrounds of arbitrary dimension. This is achieved within the canonical formalism. We consider massless fields of spin s+1/2, described by a symmetric spinor-tensor of rank s in the Fang-Fronsdal approach. We begin from a detailed analysis of the spin 5/2 example, for which we cast the Fang-Fronsdal action in Hamiltonian form, we derive the charges and we propose boundary conditions on the canonical variables that secure their finiteness. We then extend the computation of charges and the characterisation of boundary conditions to arbitrary half-integer spin. Our construction generalises to higher-spin fermionic gauge fields the known Hamiltonian derivation of supercharges in AdS supergravity., Comment: 42 pages. References added; version to appear in JHEP

Chiral tensors of mixed Young symmetry, which exist in the same spacetime dimensions $2 + 4n$ where chiral $p$-forms can be defined, are investigated. Such chiral tensors have been argued to play a central role in exotic formulations of gravity in 6 dimensions and possess intriguing properties. A variational principle that yields the chiral equations of motion is explicitly constructed and related to the action for a non-chiral tensor. The use of prepotentials turns out to be essential in our analysis. We also comment on dimensional reduction., Comment: Expanded version with 3 appendices providing explicit proofs of central results

We show that the equations of motion for (free) integer higher spin gauge fields can be formulated as twisted self-duality conditions on the higher spin curvatures of the spin-$s$ field and its dual. We focus on the case of four spacetime dimensions, but formulate our results in a manner applicable to higher spacetime dimensions. The twisted self-duality conditions are redundant and we exhibit a non-redundant subset of conditions, which have the remarkable property to involve only first-order derivatives with respect to time. This non-redundant subset equates the electric field of the spin-$s$ field (which we define) to the magnetic field of its dual (which we also define), and vice versa. The non-redundant subset of twisted self-duality conditions involve the purely spatial components of the spin-$s$ field and its dual, and also the components of the fields with one zero index. One can get rid of these gauge components by taking the curl of the equations, which does not change their physical content. In this form, the twisted self-duality conditions can be derived from a variational principle that involves prepotentials, which are the higher spin generalizations of the prepotentials previously found in the spins 2 and 3 cases. The prepotentials have again the intriguing feature of possessing both higher spin diffeomorphism invariance and higher spin conformal geometry. The tools introduced in an earlier paper for handling higher spin conformal geometry turn out to be crucial for streamlining the analysis. In four spacetime dimensions where the electric and magnetic fields are tensor fields of the same type, the twisted self-duality conditions enjoy an $SO(2)$ electric-magnetic invariance. We explicitly show that this symmetry is an "off-shell symmetry" (i.e., a symmetry of the action and not just of the equations of motion). Remarks on the extension to higher dimensions are given., Comment: Minor misprint corrected. Simplification of Hamiltonian added

We study asymptotic charges for symmetric massless higher-spin fields on Anti de Sitter backgrounds of arbitrary dimension within the canonical formalism. We first analyse in detail the spin-3 example: we cast Fronsdal's action in Hamiltonian form, we derive the charges and we propose boundary conditions on the canonical variables that secure their finiteness. We then extend the computation of charges and the characterisation of boundary conditions to arbitrary spin., Comment: 44 pages. References and comments added; version to appear in JHEP

In a recent paper (JHEP {\bf 1508} (2015) 021), we have investigated hypersymmetry bounds in the context of simple anti-de Sitter hypergravity in $2+1$ dimensions. We showed that these bounds involved non linearly the spin-$2$ and spin-$4$ charges, and were saturated by a class of extremal black holes, which are $\frac14$-hypersymmetric. We continue the analysis here by considering $(M,N)$-extended anti-de Sitter hypergravity models, based on the superalgebra $osp(M \vert 4) \oplus osp(N \vert 4)$. The asymptotic symmetry superalgebra is then the direct sum of two-copies of a $W$-superalgebra that contains $so(M)$ (or $so(N)$) Kac-Moody currents of conformal weight $1$, fermionic generators of conformal weight $5/2$ and bosonic generators of conformal weight $4$ in addition to the Virasoro generators. The nonlinear hypersymmetry bounds on the conserved charges are derived and shown to be saturated by a class of extreme hypersymmetric black holes which we explicitly construct., Comment: To appear in the Proceedings of the workshop "Higher Spin Gauge Theories", Institute for Advanced Studies, NTU, Singapore, November 4-6, 2015

We study systematically the conformal geometry of higher spin bosonic gauge fields in three spacetime dimensions. We recall the definition of the Cotton tensor for higher spins and establish a number of its properties that turn out to be key in solving in terms of prepotentials the constraint equations of the Hamiltonian (3 + 1) formulation of four-dimensional higher spin gauge fields. The prepotentials are shown to exhibit higher spin conformal symmetry. Just as for spins 1 and 2, they provide a remarkably simple, manifestly duality invariant formulation of the theory. While the higher spin conformal geometry is developed for arbitrary bosonic spin, we explicitly perform the Hamiltonian analysis and derive the solution of the constraints only in the illustrative case of spin 3. In a separate publication, the Hamiltonian analysis in terms of prepotentials is extended to all bosonic higher spins using the conformal tools of this paper, and the same emergence of higher spin conformal symmetry is confirmed., Comment: 32 pages, typos in formulas (3.3), (3.5), (7.3) and (7.4) corrected

We investigate the hypersymmetry bounds on the higher spin black hole parameters that follow from the asymptotic symmetry superalgebra in higher-spin anti-de Sitter gravity in three spacetime dimensions. We consider anti-de Sitter hypergravity for which the analysis is most transparent. This is a $osp(1\vert 4) \oplus osp(1\vert 4)$ Chern-Simons theory which contains, besides a spin-$2$ field, a spin-$4$ field and a spin-$5/2$ field. The asymptotic symmetry superalgebra is then the direct sum of two-copies of the hypersymmetric extension $W_{(2,\frac52,4)}$ of $W_{(2,4)}$, which contains fermionic generators of conformal weight $5/2$ and bosonic generators of conformal weight $4$ in addition to the Virasoro generators. Following standard methods, we derive bounds on the conserved charges from the anticommutator of the hypersymmetry generators. The hypersymmetry bounds are nonlinear and are saturated by the hypersymmetric black holes, which turn out to possess $1/4$-hypersymmetry and to be "extreme", where extremality can be defined in terms of the entropy: extreme black holes are those that fulfill the extremality bounds beyond which the entropy ceases to be a real function of the black hole parameters. We also extend the analysis to other $sp(4)$-solitonic solutions which are maximally (hyper)symmetric., Comment: 26 pages

We study the role of Chern--Simons couplings for the appearance of enhanced symmetries of Cremmer--Julia type in various theories. It is shown explicitly that for generic values of the Chern--Simons coupling there is only a parabolic Lie subgroup of symmetries after reduction to three space-time dimensions but that this parabolic Lie group gets enhanced to the full and larger Cremmer--Julia Lie group of hidden symmetries if the coupling takes a specific value. This is heralded by an enhanced isotropy group of the metric on the scalar manifold. Examples of this phenomenon are discussed as well as the relation to supersymmetry. Our results are also connected with rigidity theorems of Borel-like algebras., Comment: To appear in the Proceedings of the 9th Workshop and School on "Quantum Field Theory and Hamiltonian Systems", 24-28 September 2014, Sinaia, Romania

We investigate the conjectured infinite-dimensional hidden symmetries of six-dimensional chiral supergravity coupled to two vector multiplets and two tensor multiplets, which is known to possess the $F_{4,4}$ symmetry upon dimensional reduction to three spacetime dimensions. Two things are done. (i) First, we analyze the geodesic equations on the coset space $F_{4,4}^{++}/K(F_{4,4}^{++})$ using the level decomposition associated with the subalgebra $\mathfrak{gl}(5)\oplus \mathfrak{sl}(2)$ of $F_{4,4}^{++}$ and show their equivalence with the bosonic equations of motion of six-dimensional chiral supergravity up to the level where the dual graviton appears. In particular, the self-duality condition on the chiral $2$-form is automatically implemented in the sense that no dual potential appears for that $2$-form, in contradistinction with what occurs for the non chiral $p$-forms. (ii) Second, we describe the $p$-form hierarchy of the model in terms of its $V$-duality Borcherds superalgebra, of which we compute the Cartan matrix., Comment: 31 pages. v2: Error in section 6.3 corrected, Dynkin diagram now appears correctly, minor typos

The asymptotic structure of three-dimensional higher-spin anti-de Sitter gravity is analyzed in the metric approach, in which the fields are described by completely symmetric tensors and the dynamics is determined by the standard Einstein-Fronsdal action improved by higher order terms that secure gauge invariance. Precise boundary conditions are given on the fields. The asymptotic symmetries are computed and shown to form a non-linear W-algebra, in complete agreement with what was found in the Chern-Simons formulation. The W-symmetry generators are two-dimensional traceless and divergenceless rank-s symmetric tensor densities of weight s (s = 2, 3, ...), while asymptotic symmetries emerge at infinity through the conformal Killing vector and conformal Killing tensor equations on the two-dimensional boundary, the solution space of which is infinite-dimensional. For definiteness, only the spin 3 and spin 4 cases are considered, but these illustrate the features of the general case: emergence of the W-extended conformal structure, importance of the improvement terms in the action that maintain gauge invariance, necessity of the higher spin gauge transformations of the metric, role of field redefinitions., Comment: 74 pages. References amended and typos corrected. Version to appear in JHEP