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K. G. Arun et al., The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of gravitational waves can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas., E. Berti is supported by NSF Grants No. PHY-1912550 and AST-2006538, NASA ATP Grants No. 17-ATP17-0225 and 19-ATP19-0051, NSF-XSEDE Grant No. PHY-090003, and NSF Grant PHY-20043. D. Blas is supported by a ‘Ayuda Beatriz Galindo Senior’ from the Spanish ‘Ministerio de Universidades’, grant BG20/00228. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. The research leading of to these results has received funding from the Spanish Ministry of Science and Innovation (PID2020-115845GB-I00/AEI/10.13039/501100011033). K. Clough is supported by funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 693024). A. Cárdenas-Avendaño acknowledges funding from the Fundación Universitaria Konrad Lorenz (Project 5INV1) and from Will and Kacie Snellings. M. Crisostomi and E. Barausse are supported by the European Union’s H2020 ERC Consolidator Grant “GRavity from Astrophysical to Microscopic Scales” (Grant No. GRAMS-815673). P. Fleury received the support of a fellowship from “la Caixa” Foundation (ID 100010434). The fellowship code is LCF/BQ/PI19/11690018. C. Herdeiro thanks the support of the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020, the projects PTDC/FIS-OUT/28407/2017, CERN/FIS-PAR/0027/2019, PTDC/FIS-AST/3041/2020 and the European Union’s Horizon 2020 research and innovation (RISE) programme H2020-MSCA-RISE-2017 Grant No. FunFiCO-777740. P. Pani and E. Maggio acknowledge financial support provided under the European Union’s H2020 ERC, Starting Grant agreement no. DarkGRA–757480, and under the MIUR PRIN and FARE programmes (GW-NEXT, CUP: B84I20000100001), and support from the Amaldi Research Center funded by the MIUR program “Dipartimento di Eccellenza” (CUP: B81I18001170001). N.Frusciante was supported by Fundação para a Ciência e a Tecnologia (FCT) through the research grants UIDB/04434/2020, UIDP/04434/2020, PTDC/FIS-OUT/29048/2017, CERN/FIS-PAR/0037/2019, the FCT project “CosmoTests—Cosmological tests of gravity theories beyond General Relativity” with ref. number CEECIND/00017/2018 and the FCT project “BEYLA –BEYond LAmbda” with ref. number PTDC/FIS-AST/0054/2021. L.Lombriser was supported by a Swiss National Science Foundation Professorship grant (No. 170547). S.N. acknowledges support from the Alexander von Humboldt Foundation. D.N. acknowledges support from the NSF Grant No. PHY-2011784. R.B. acknowledges financial support from FCT – Fundação para a Ciência e a Tecnologia, I.P., under the Scientific Employment Stimulus - Individual Call - 2020.00470.CEECIND. V. Paschalidis acknowledges support from NSF Grant PHY-1912619 and NASA Grant 80NSSC20K1542 to the University of Arizona. B.S.S. is supported by NSF grants No. AST-2006384 and PHY-2012083. C.F.S. is supported by contracts ESP2017-90084-P and PID2019-106515GB-I00/AEI/10.13039/501100011033 (Spanish Ministry of Science and Innovation) and 2017-SGR-1469 (AGAUR, Generalitat de Catalunya). T. P. S. acknowledges partial support from the STFC Consolidated Grant No. ST/P000703/1. M. Ruiz acknowledges support from NASA Grant 80NSSC17K0070 to the University of Illinois at Urbana-Champaign. I.D. Saltas is supported by the Czech Science Foundation GAČR, Grant No. 21-16583M. N. Stergioulas is supported by the ESA Prodex grant PEA:4000132310 “LISA Stochastic Signals Analysis Pipeline”. F.V. acknowledges partial support from CNES. K.Y. acknowledges support from NSF Grant PHY-1806776, NASA Grant 80NSSC20K0523, a Sloan Foundation Research Fellowship and the Owens Family Foundation. K.Y. would like to also acknowledge support by the COST Action GWverse CA16104 and JSPS KAKENHI Grants No. JP17H06358. N. Yunes acknowledges support from NASA Grants No. NNX16AB98G, 80NSSC17M0041 and 80NSSC18K1352, NSF Award No. 1759615, and the Simons Foundation through MPS Award Number 896696. D.D. acknowledge financial support via an Emmy Noether Research Group funded by the German Research Foundation (DFG) under grant no. DO 1771/1-1.

A variant of the ADT method for the determination of gravitational charges as integrals at infinity is applied to "Chern-Simons-like" theories of 3D gravity, and the result is used to find the mass and angular momentum of the BTZ black hole considered as a solution of a variety of massive 3D gravity field equations. The results agree with many obtained previously by other methods, including our own results for "Minimal Massive Gravity", but they disagree with others, including recently reported results for "Exotic Massive Gravity". We also find the central charges of the asymptotic conformal symmetry algebra for the generic 3D gravity model with AdS vacuum and discuss implications for black hole thermodynamics., 26 pages; v2, references added

We show how Newton-Cartan geometry can be generalized to String Newton-Cartan geometry which is the geometry underlying non-relativistic string theory. Several salient properties of non-relativistic string theory in this geometric background are presented and a discussion of possible research for the future is outlined.

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 discuss non-relativistic limits of general relativity. In particular, we define a special fine-tuned non-relativistic limit, inspired by string theory, where the Einstein-Hilbert action has been supplemented by the kinetic term of a one-form gauge field. Taking the limit, a crucial cancellation takes place, in an expansion of the action in terms of powers of the velocity of light, between a leading divergence coming from the spin-connection squared term and another infinity that originates from the kinetic term of the one-form gauge field such that the finite invariant non-relativistic gravity action is given by the next subleading term. This non-relativistic action allows an underlying torsional Newton-Cartan geometry as opposed to the zero torsion Newton-Cartan geometry that follows from a more standard limit of General Relativity but it lacks the Poisson equation for the Newton potential. We will mention extensions of the model to include this Poisson equation.

We show how Newton-Cartan gravity can be generalized to String Newton-Cartan gravity which is identified as the proper geometry underlying non-relativistic string theory. Specific properties of non-relativistic string theory are discussed such as T-duality and (solutions to) the equations of motion of the background fields.

We show that our previous work on Galilei and Carroll gravity, apt for particles, can be generalized to Galilei and Carroll gravity theories adapted to p-branes (p = 0, 1, 2, ...). Within this wider brane perspective, we make use of a formal map, given in the literature, between the corresponding p-brane Carroll and Galilei algebras where the index describing the directions longitudinal (transverse) to the Galilei brane is interchanged with the index covering the directions transverse (longitudinal) to the Carroll brane with the understanding that the time coordinate is always among the longitudinal directions. This leads among other things in 3D to a map between Galilei particles and Carroll strings and in 4D to a similar map between Galilei strings and Carroll strings. We show that this formal map extends to the corresponding Lie algebra expansion of the Poincar\'e algebra and, therefore, to several extensions of the Carroll and Galilei algebras including central extensions. We use this formal map to construct several new examples of Carroll gravity actions. Furthermore, we discuss the symmetry between Carroll and Galilei at the level of the p-brane sigma model action and apply this formal symmetry to give several examples of 3D and 4D particles and strings in a curved Carroll background., Comment: 20 pages

We perform an exotic dualization of the Ramond-Ramond fields in type II double field theory, in which they are encoded in a Majorana-Weyl spinor of O(D,D). Starting from a first-order master action, the dual theory in terms of a tensor-spinor of O(D,D) is determined. This tensor-spinor is subject to an exotic version of the (self-)duality constraint needed for a democratic formulation. We show that in components, reducing O(D,D) to GL(D), one obtains the expected exotically dual theory in terms of mixed Young tableaux fields. To this end, we generalize exotic dualizations to self-dual fields, such as the 4-form in type IIB string theory., 14 pages, v2: refs. added, to appear in PLB

We show that a recently proposed action for three-dimensional non-relativistic gravity can be obtained by taking the limit of a relativistic Lagrangian that involves the co-adjoint Poincare algebra. We point out the similarity of our construction with the way that three-dimensional Galilei Gravity and Extended Bargmann Gravity can be obtained by taking the limit of a relativistic Lagrangian that involves the Poincare algebra. We extend our results to the AdS case and we will see that there is a chiral decomposition both at the relativistic and non-relativistic level. We comment on possible further generalizations., Comment: 28 pages

We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on Lorentzian manifolds and the Killing spinor equations that their supersymmetry parameters obey. This gives rise to a set of algebraic and differential Killing spinor equations that are obeyed by the supersymmetry parameters of the resulting three-dimensional non-relativistic field theories. We derive necessary and sufficient conditions that determine whether a Newton-Cartan background admits non-trivial solutions of these Killing spinor equations. Two classes of examples of Newton-Cartan backgrounds that obey these conditions are discussed. The first class is characterised by an integrable foliation, corresponding to so-called twistless torsional geometries, and includes manifolds whose spatial slices are isomorphic to the Poincar\'e disc. The second class of examples has a non-integrable foliation structure and corresponds to contact manifolds., Comment: 43 pages

We show that the general method of Lie algebra expansions can be applied to re-construct several algebras and related actions for non-relativistic gravity that have occurred in the recent literature. We explain the method and illustrate its applications by giving several explicit examples. The method can be generalized to include ultra-relativistic gravity and non-relativistic supergravity as well., This work and LR have been supported in part by the MINECO/FEDER, UE grant FPA2015-66793-P and by the Spanish Research Agency (Agencia Estatal de Investigaci´on) through the grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597. JMI has been supported by the grants MTM2014-57129-C2-1-P from the MINECO (Spain), VA137G18 Spanish Junta de Castilla y Le´on and FEDER BU229P18. TO wishes to thank M.M. Fern´andez for her permanent support. EB wishes to thank the Instituto de F´ısica Te´orica UAM/CSIC of Madrid for hospitality.

We identify the proper geometry underlying non-relativistic string theory as 'String Newton-Cartan Gravity'. It has the distinguishing feature that one-dimensional foliation in Newton-Cartan geometry is replaced by a two-dimensional foliation on the target space. We discuss some basic properties of the string Newton-Cartan space-time, in particular it's behaviour under T-duality transformations. This leads to interesting non-relativistic conformal field theories at the boundary that have applications in condensed matter physics.

Nonrelativistic string theory is described by a sigma model with a relativistic worldsheet and a nonrelativistic target spacetime geometry, that is called string Newton-Cartan geometry. In this paper we obtain string Newton-Cartan geometry as a limit of the Riemannian geometry of General Relativity with a fluxless two-form field. We then apply the same limit to relativistic string theory in curved background fields and show that it leads to nonrelativistic string theory in a string Newton-Cartan geometry coupled to a Kalb-Ramond and dilaton field background. Finally, we use our limiting procedure to study the spacetime equations of motion and the T-duality transformations of nonrelativistic string theory. Our results reproduce the recent studies of beta-functions and T-duality of nonrelativistic string theory obtained from the microscopic worldsheet definition of nonrelativistic string theory., 41 pages

The non-relativistic version of General Relativity, called Newton-Cartan gravity, has received renewed attention as a tool to explore (non-perturbative) properties of non-relativistic quantum field theories. The first part of this talk is a non-specialist introduction to Newton-Cartan geometry; in particular, it is shown how Newton-Cartan gravity arises as a special limit of General Relativity. The second part reviews a novel non-relativistic limit of the 3D massive spin-2 Fierz-Pauli theory to a spin-2 planar Schrodinger equation that has been proposed to describe the so-called GMP gapped spin-2 mode of fractional Quantum Hall states. The talk concludes with speculations on an extension of this non-relativistic limit to interacting massive 3D gravity theories.

We show how the Wess-Zumino terms of the different branes in string theory can be embedded within double field theory. Crucial ingredients in our construction are the identification of the correct brane charge tensors and the use of the double field theory potentials that arise from dualizing the standard double field theory fields. This leads to a picture where under T-duality the brane does not change its worldvolume directions but where, instead, it shows different faces depending on whether some of the worldvolume and/or transverse directions invade the winding space. As a non-trivial by-product we show how the different Wess-Zumino terms are modified when the brane propagates in a background with a non-zero Romans mass parameter. Furthermore, we show that for non-zero mass parameter the brane creation process, when one brane passes through another brane, gets generalized to brane configurations that involve exotic branes as well., SCOPUS: ar.j, info:eu-repo/semantics/published

We construct an action for four-dimensional extended string Newton-Cartan gravity which is an extension of the string Newton-Cartan gravity that underlies nonrelativistic string theory. The action can be obtained as a nonrelativistic limit of the Einstein-Hilbert action in General Relativity augmented with a term that contains an auxiliary two-form and one-form gauge field that both have zero flux on-shell. The four-dimensional extended string Newton-Cartan gravity is based on a central extension of the algebra that underlies string Newton-Cartan gravity. The construction is similar to the earlier construction of a three-dimensional Chern-Simons action for extended Newton-Cartan gravity, which is based on a central extension of the algebra that underlies Newton-Cartan gravity. We show that this three-dimensional action is naturally obtained from the four-dimensional action by a reduction over the spatial isometry direction longitudinal to the string followed by a truncation of the extended string Newton-Cartan gravity fields. Our construction can be seen as a special case of the construction of an action for extended p-brane Newton-Cartan gravity in p+3 dimensions., Comment: 16 pages; v2: references added; v3: 18 pages, published version

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.

After a brief discussion of RR and NS fluxes, we consider the T-duality family of fluxes whose prototype is the Scherk-Schwarz reduction of the S-dual of the RR scalar of IIB supergravity. We give a complete classification of these fluxes, including the ones that are non-geometric, and we explain their relation with dual mixed-symmetry potentials. We point out that the non-geometric fluxes turn out to be dual to potentials containing nine antisymmetric indices. Our analysis suggests that all these fluxes can be understood in the context of double field theory, although for the non-geometric ones one expects a violation of the strong constraint.

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

We construct a N = 2 supersymmetric extension of Newton-Cartan gravity by gauging a N = 2 supersymmetric extension of the Bargmann algebra. Due to technical complications we restrict the construction to the three-dimensional case. We discuss the gauge-fixing of the resulting Newton-Cartan supergravity theory to a Galilean supergravity that contains the Newton potential. An unusual feature is that, in order to realize the supersymmetry on the Newton potential, we need to introduce a dual Newton potential as well. Together, Newton potential and dual potential, they form a holomorphic function of the two spatial coordinates. We briefly discuss the four-dimensional case.

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.

We compare the gauging of the Bargmann algebra, for the case of arbitrary torsion, with the result that one obtains from a null-reduction of General Relativity. Whereas the two procedures lead to the same result for Newton-Cartan geometry with arbitrary torsion, the null-reduction of the Einstein equations necessarily leads to Newton-Cartan gravity with zero torsion. We show, for three space-time dimensions, how Newton-Cartan gravity with arbitrary torsion can be obtained by starting from a Schroedinger field theory with dynamical exponent z=2 for a complex compensating scalar and next coupling this field theory to a z=2 Schroedinger geometry with arbitrary torsion. The latter theory can be obtained from either a gauging of the Schroedinger algebra, for arbitrary torsion, or from a null-reduction of conformal gravity., 21 pages

Having in mind applications to Condensed Matter Physics, we perform a null-reduction of General Relativity in d+1 spacetime dimensions thereby obtaining an extension to arbitrary torsion of the twistless-torsional Newton-Cartan geometry. We shortly discuss the implementation of the equations of motion.

In this presentation we give a short overview of Newton-Cartan geometry and gravity and some recent results about its matter couplings.

In this paper we show that the number of all 1/2-BPS branes in string theory compactified on a torus can be derived by universal wrapping rules whose formulation we present. These rules even apply to branes in less than ten dimensions whose ten-dimensional origin is an exotic brane. In that case the wrapping rules contain an additional combinatorial factor that is related to the highest dimension in which the ten-dimensional exotic brane, after compactification, can be realized as a standard brane. We show that the wrapping rules also apply to cases with less supersymmetry. As a specific example, we discuss the compactification of IIA/IIB string theory on $(T^4/{\mathbb{Z}_2}) \times T^n$., Comment: 21 pages

We discuss a non-relativistic contraction of massive and massless field theories minimally coupled to gravity. Using the non-relativistic limiting procedure introduced in our previous work, we (re-)derive non-relativistic field theories of massive and massless spins 0 to 3/2 coupled to torsionless Newton-Cartan backgrounds. We elucidate the relativistic origin of the Newton-Cartan central charge gauge field $m_\mu$ and explain its relation to particle number conservation., Comment: 19 pages

We give a short overview of Newton–Cartan geometry and gravity including its matter couplings. We also present results on a new non-relativistic gravity model in three spacetime dimensions, called extended Bargmann gravity, and show that this model has matter couplings that differ from those of Newton–Cartan gravity.

Motivated by recent applications of Carroll symmetries we investigate the geometry of flat and curved (AdS) Carroll space and the symmetries of a particle moving in such a space both in the bosonic as well as in the supersymmetric case. In the bosonic case we find that the Carroll particle possesses an infinite-dimensional symmetry which only in the flat case includes dilatations. The duality between the Bargmann and Carroll algebra, relevant for the flat case, does not extend to the curved case. In the supersymmetric case we study the dynamics of the N=1 AdS Carroll superparticle. Only in the flat limit we find that the action is invariant under an infinite-dimensional symmetry that includes a supersymmetric extension of the Lifshitz Carroll algebra with dynamical exponent z=0. We also discuss in the flat case the extension to N=2 supersymmetry and show that the flat N=2 superparticle is equivalent to the (non-moving) N=1 superparticle and that therefore it is not BPS unlike its Galilei counterpart. This is due to the fact that in this case kappa-symmetry eliminates the linearized supersymmetry. In an appendix we discuss the N=2 curved case in three dimensions only and show that there are two N=2 theories that are physically different., 35 pages; v1

We show that the solitonic branes of ten-dimensional IIA/IIB string theory must satisfy, upon toroidal compactification, a specific wrapping rule in order to reproduce the number of half-supersymmetric solitonic branes that follows from a supergravity analysis. The realization of this wrapping rule suggests that IIA/IIB string theory contains a whole class of so-called "non-standard" Kaluza-Klein monopoles.

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

We discuss some general properties of "defect branes", i.e. branes of co-dimension two, in (toroidally compactified) IIA/IIB string theory. In particular, we give a full classification of the supersymmetric defect branes in dimensions 2 < D < 11 as well as their higher-dimensionalstring and M-theory origin as branes and a set of "generalized" Kaluza-Klein monopoles. We point out a relation between the generalized Kaluza-Klein monopole solutions and a particular type of mixed-symmetry tensors. These mixed-symmetry tensors can be defined at the linearized level as duals of the supergravity potentials that describe propagating degrees of freedom. It is noted that the number of supersymmetric defect branes is always twice the number of corresponding central charges in the supersymmetry algebra., Latex2e paper, 28 pages, no figures. Footnote added

We consider the D-branes that occur in IIA/IIB string theory compactified on a torus. We review how a general expression for the Wess-Zumino term of such branes is derived. We also review the method to determine the D-brane Wess-Zumino term in a U-duality covariant way, and we apply it to derive all the branes obtained by transforming the D-branes under U-duality in any dimension above five. We finally determine all the supersymmetric branes supporting worldvolume tensor multiplets that occur in these theories in any dimension.

We probe doubled geometry with dual fundamental branes, i.e. solitons. Restricting ourselves first to solitonic branes with more than two transverse directions we find that the doubled geometry requires an effective wrapping rule for the solitonic branes which is dual to the wrapping rule for fundamental branes. This dual wrapping rule can be understood by the presence of Kaluza-Klein monopoles. Extending our analysis to supersymmetric solitonic branes with less than or equal to two transverse directions we show that such solitons are precisely obtained by applying the same dual wrapping rule to these cases as well. This extended wrapping rule can not be explained by the standard Kaluza-Klein monopole alone. Instead, it suggests the existence of a class of generalized Kaluza-Klein monopoles in ten-dimensional string theory., 16 pages

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

We show how superconformal gaugings in three dimensions can be systematically constructed using the embedding tensor technique. These gaugings have been argued to describe the worldvolume theory of multiple M2-branes. Applying our technique we construct the most general superconformal gaugings with N = 5, 6 and 8 supersymmetry. In the case of N = 5 supersymmetry we find three exceptional gaugings. We briefly discuss new developments concerning the massive deformations of the superconformal gauge theories. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

42 pages., We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of the same fields in the tensor hierarchy., The Center for Research and Education in Fundamental Physics is supported by the “Innovations- und Kooperationsprojekt C-13” of the Schweizerische Universitaetskonferenz SUK/CRUS. This work has been supported in part by the INTAS Project 1000008-7928, the Spanish Ministry of Science and Education grants FPU AP2004-2574 (MH), FPA2006-00783 (MH and TO), the Comunidad de Madrid grant HEPHACOS P-ESP-00346 (MH and TO), the Spanish Consolider-Ingenio 2010 program CPAN CSD2007-00042 (MH and TO) and by the EU Research Training Network Constituents, Fundamental Forces and Symmetries of the Universe MRTN-CT-2004-005104. This work is part of the research programme of the ‘Stichting voor Fundamenteel Onderzoek der Materie (FOM)’. Further, TO wishes to express his gratitude to M.M. Fern´andez for her unwavering support., JH was supported by a research grant of the Swiss National Science Foundation and wishes to thank the Instituto de F´ısica Te´orica of the Universidad Aut´onoma de Madrid for its hospitality. The Center for Research and Education in Fundamental Physics is supported by the “Innovations- und Kooperationsprojekt C-13” of the Schweizerische Universitaetskonferenz SUK/CRUS. This work has been supported in part by the INTAS Project 1000008-7928, the Spanish Ministry of Science and Education grants FPU AP2004-2574 (MH), FPA2006-00783 (MH and TO), the Comunidad de Madrid grant HEPHACOS P-ESP-00346 (MH and TO), the Spanish Consolider-Ingenio 2010 program CPAN CSD2007-00042 (MH and TO) and by the EU Research Training Network Con- stituents, Fundamental Forces and Symmetries of the Universe MRTN-CT-2004-005104. This work is part of the research programme of the ‘Stichting voor Fundamenteel Onderzoek der Materie (FOM)’. Further, TO wishes to express his gratitude to M.M. Fern´andez for her unwavering support.

We consider the problem of finding a dual formulation of gravity in the presence of non-trivial matter couplings. In the absence of matter a dual graviton can be introduced only for linearised gravitational interactions. We show that the coupling of linearised gravity to matter poses obstructions to the usual construction and comment on possible resolutions of this difficulty., SCOPUS: ar.j, info:eu-repo/semantics/published

We show that three-dimensional General Relativity, augmented with two vector fields, allows for a non-relativistic limit, different from the standard limit leading to Newtonian gravity, that results into a well-defined action which is of the Chern-Simons type. We show that this three-dimensional `Extended Bargmann Gravity', after coupling to matter, leads to equations of motion allowing a wider class of background geometries than the ones that one encounters in Newtonian gravity. We give the supersymmetric generalization of these results and point out an important application in the context of calculating partition functions of non-relativistic field theories using localization techniques., Comment: 6 pages, v2: typo's corrected, reference updated, accepted for publication in Phys. Rev. Lett

We initiate the study of non- and ultra-relativistic higher spin theories. For sake of simplicity we focus on the spin-3 case in three dimensions. We classify all kinematical algebras that can be obtained by all possible In\"on\"u--Wigner contraction procedures of the kinematical algebra of spin-3 theory in three dimensional (anti-) de Sitter space-time. We demonstrate how to construct associated actions of Chern--Simons type, directly in the ultra-relativistic case and by suitable algebraic extensions in the non-relativistic case. We show how to give these kinematical algebras an infinite-dimensional lift by imposing suitable boundary conditions in a theory we call "Carroll Gravity", whose asymptotic symmetry algebra turns out to be an infinite-dimensional extension of the Carroll algebra., Comment: 32+12 pages, 2 figures; v2: 1 footnote, 4 refs; v3: 1 ref corrected, 1 ref updated

In order to construct globally well-defined 7-brane solutions we postulate the existence of a new type of 7-brane. We show that these new 7-branes play an important role in understanding both the existing F-theory 7-brane configurations as well as more general 7-brane configurations. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

We derive a torsionfull version of three-dimensional $$ \mathcal{N}=2 $$ Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The “superconformal” theory that we start with is Schrodinger supergravity which we obtain by gauging the Schrodinger superalgebra. We present two non-relativistic $$ \mathcal{N}=2 $$ matter multiplets that can be used as compensators in the superconformal calculus. They lead to two different off-shell formulations which, in analogy with the relativistic case, we call “old minimal” and “new minimal” Newton-Cartan supergravity. We find similarities but also point out some differences with respect to the relativistic case.

There exists two distinct off-shell $$ \mathcal{N} $$ = 2 supergravities in three dimensions. They are also referred to as $$ \mathcal{N} $$ = (1, 1) and $$ \mathcal{N} $$ = (2, 0) supergravities, and they arise from the coupling of the Weyl multiplet to a compensating scalar or vector multiplet, respectively, followed by fixing of conformal symmetries. The $$ \mathcal{N} $$ = (p, q) terminology refers to the underlying anti-de Sitter superalgebras OSp(2, p) ⊕ OSp(2, q) with R-symmetry group SO(p) × SO(q). We construct off-shell invariants of these theories up to fourth order in derivatives. As an application of these results, we determine the special combinations of the $$ \mathcal{N} $$ = (1, 1) invariants that admit anti-de Sitter vacuum solution about which there is a ghost-free massive spin-2 multiplet of propagating modes. We also show that the $$ \mathcal{N} $$ =(2,0) invariants do not allow such possibility.

The role of the $$ \overline{\mathrm{D}3} $$ brane in providing de Sitter vacua with spontaneously broken supersymmetry in the KKLT construction is clarified. The first step in this direction was explained in [1, 2]: it was shown there that in the GKP background the bosonic contributions to the vacuum energy from the DBI and WZ term cancel for a D3 brane, but double for a $$ \overline{\mathrm{D}3} $$ brane, leading to de Sitter vacua. The next step was taken in [3] where the analogous mechanism of the doubling (cancelation) of the $$ \overline{\mathrm{D}3} $$ (D3) DBI and WZ terms was discovered in the presence of Volkov-Akulov fermions living on the brane, in a flat supergravity background. Here we confirm this mechanism of doubling/cancelation for the $$ \overline{\mathrm{D}3} $$ /D3 brane in the GKP supergravity background preserving $$ \mathcal{N} $$ = 1, d = 4 supersymmetry. We find that imaginary self-dual G (3) flux of type (2, 1) nicely removes the SU(3) fermion triplet by giving it a large mass, while leaving the Volkov-Akulov goldstino, which is the SU(3) singlet, massless. This makes the de Sitter landscape in D-brane physics clearly related to de Sitter vacua in effective d = 4 supergravity with a nilpotent multiplet and spontaneously broken supersymmetry.

Using an off-shell Killing spinor analysis we perform a systematic investigation of the supersymmetric background and black hole solutions of the $$ \mathcal{N}=\left(1,\;1\right) $$ Cosmological New Massive Gravity model. The solutions with a null Killing vector are the same pp-wave solutions that one finds in the $$ \mathcal{N}=1 $$ model but we find new solutions with a time-like Killing vector that are absent in the $$ \mathcal{N}=1 $$ case. An example of such a solution is a Lifshitz spacetime. We also consider the supersymmetry properties of the so-called rotating hairy BTZ black holes and logarithmic black holes in an AdS 3 background. Furthermore, we show that under certain assumptions there is no supersymmetric Lifshitz black hole solution.

We discuss the relation between generalised fluxes and mixed-symmetry potentials. We first consider the NS fluxes, and point out that the `non-geometric' $R$ flux is dual to a mixed-symmetry potential with a set of nine antisymmetric indices. We then consider the T-duality family of fluxes whose prototype is the Scherk-Schwarz reduction of the S-dual of the RR scalar of IIB supergravity. Using the relation with mixed-symmetry potentials, we are able to give a complete classification of these fluxes, including the ones that are non-geometric. The non-geometric fluxes again turn out to be dual to potentials containing nine antisymmetric indices. Our analysis suggests that all these fluxes can be understood in the context of double field theory, although for the non-geometric ones one expects a violation of the strong constraint., 19 pages, refs. added