In this work we study a non-relativistic three dimensional Chern-Simons gravity theory based on an enlargement of the Extended Bargmann algebra. A finite nonrelativistic Chern-Simons gravity action is obtained through the non-relativistic contraction of a particular U(1) enlargement of the so-called AdS-Lorentz algebra. We show that the non-relativistic gravity theory introduced here reproduces the Maxwellian Exotic Bargmann gravity theory when a flat limit l → ∞ is applied. We also present an alternative procedure to obtain the non-relativistic versions of the AdS-Lorentz and Maxwell algebras through the semigroup expansion method.

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Non-relativistic gravity theory based on an enlargement of the extended Bargmann algebra

We study N = (2, 4, 8) supersymmetric extensions of the three dimensional BMS algebra (BMS3) with most generic possible central extensions. We find that N - extended supersymmetric BMS3 algebras can be derived by a suitable contraction of two copies of the extended superconformal algebras. Extended algebras from all the consistent contractions are obtained by scaling left-moving and right-moving supersymmetry generators symmetrically, while Virasoro and R-symmetry generators are scaled asymmetrically. On the way, we find that the BMS/GCA correspondence does not in general hold for supersymmetric systems. Using the β-γ and the $$ \mathfrak{b}\hbox{-} \mathfrak{c} $$
 systems, we construct free field realisations of all the extended super-BMS3 algebras.

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Extended supersymmetric BMS3 algebras and their free field realisations

We show that an extended 3D Schrodinger algebra introduced in [1] can be reformulated as a 3D Poincare algebra extended with an SO(2) R-symmetry generator and an SO(2) doublet of bosonic spin-1/2 generators whose commutator closes on 3D translations and a central element. As such, a non-relativistic Chern-Simons theory based on the extended Schrodinger algebra studied in [1] can be reinterpreted as a relativistic Chern-Simons theory. The latter can be obtained by a contraction of the SU(1, 2) × SU(1, 2) Chern-Simons theory with a non principal embedding of SL(2, ℝ) into SU(1, 2). The non-relativisic Schrodinger gravity of [1] and its extended Poincare gravity counterpart are obtained by choosing different asymptotic (boundary) conditions in the Chern-Simons theory. We also consider extensions of a class of so-called l-conformal Galilean algebras, which includes the Schrodinger algebra as its member with l = 1/2, and construct ChernSimons higher-spin gravities based on these algebras.

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Three-dimensional (higher-spin) gravities with extended Schrödinger and l-conformal Galilean symmetries

Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra

Generalized maxwellian exotic bargmann gravity theory in three spacetime dimensions

We study three-dimensional non-linear models of vector and vector-spinor Goldstone fields associated with the spontaneous breaking of certain higher-spin counterparts of supersymmetry whose Lagrangians are of a Volkov-Akulov type. Goldstone fields in these models transform non-linearly under the spontaneously broken rigid symmetries. We find that the leading term in the action of the vector Goldstone model is the Abelian Chern-Simons action whose gauge symmetry is broken by a quartic term. As a result, the model has a propagating degree of freedom which, in a decoupling limit, is a quartic Galileon scalar field. The vector-spinor goldstino model turns out to be a non-linear generalization of the three-dimensional Rarita-Schwinger action. In contrast to the vector Goldstone case, this non-linear model retains the gauge symmetry of the Rarita-Schwinger action and eventually reduces to the latter by a non-linear field redefinition. We thus find that the free Rarita-Schwinger action is invariant under a hidden rigid super-symmetry generated by fermionic vector-spinor operators and acting non-linearly on the Rarita-Schwinger goldstino.

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Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?

We study three-dimensional non-linear models of vector and vector-spinor Goldstone fields associated with the spontaneous breaking of certain higher-spin counterparts of supersymmetry whose Lagrangians are of a Volkov-Akulov type. Goldstone fields in these models transform non-linearly under the spontaneously broken rigid symmetries. We find that the leading term in the action of the vector Goldstone model is the Abelian Chern-Simons action whose gauge symmetry is broken by a quartic term. As a result, the model has a propagating degree of freedom which, in a decoupling limit, is a quartic Galileon scalar field. The vector-spinor goldstino model turns out to be a non-linear generalization of the three-dimensional Rarita-Schwinger action. In contrast to the vector Goldstone case, this non-linear model retains the gauge symmetry of the Rarita-Schwinger action and eventually reduces to the latter by a non-linear field redefinition. We thus find that the free Rarita-Schwinger action is invariant under a hidden rigid supersymmetry generated by fermionic vector-spinor operators and acting non-linearly on the Rarita-Schwinger goldstino.

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We show the equality between macroscopic and microscopic (statistical) black hole entropy for a class of four dimensional non-supersymmetric black holes in $$ \mathcal{N} $$
 = 2 supergravity theory, up to the first subleading order in their charges. This solves a long standing entropy puzzle for this class of black holes. The macroscopic entropy has been computed in the presence of a newly derived higher-derivative supersymmetric invariant of [1], connected to the five dimensional supersymmetric Weyl squared Lagrangian. Microscopically, the crucial role in obtaining the equivalence is played by the anomalous gauge gravitational Chern-Simons term.

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The resolution of an entropy puzzle for 4D non-BPS black holes

Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the generalisation of unimodular gravity to supergravity using a super-Stuckelberg mechanism. In this paper, we make a connection between this new approach and the previous two which are in the context of nilpotent superfields and the goldstino brane. We show that upon appropriate field redefinitions, the 4D actions match up to the cubic order in the fields. This points at the possible existence of a more general framework to obtain de Sitter spacetimes from high-energy theories.

Unimodular vs Nilpotent Superfield Approach to Pure dS Supergravity

We explore the properties of polynomial Lagrangians for chiral p-forms previously proposed by the last named author, and in particular, provide a self-contained treatment of the symmetries and equations of motion that shows a great economy and simplicity of this formalism. We further use analogous techniques to construct polynomial democratic Lagrangians for general p-forms where electric and magnetic potentials appear on equal footing as explicit dynamical variables. Due to our reliance on the differential form notation, the construction is compact and universally valid for forms of all ranks, in any number of dimensions.

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Sukruti Bansal

Papers

Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?

Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?

The resolution of an entropy puzzle for 4D non-BPS black holes

Unimodular vs Nilpotent Superfield Approach to Pure dS Supergravity

Polynomial duality-symmetric lagrangians for free p-forms