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Journal ArticleDOI

Hypersymmetric extensions of Maxwell-Chern-Simons gravity in 2+1 dimensions

TL;DR: In this article, a consistent way of coupling three-dimensional hyper-Maxwell-Chern-Simons gravity theory with massless spin-$\frac{5}{2}$ gauge fields was presented.
Abstract: We present a consistent way of coupling three-dimensional Maxwell-Chern-Simons gravity theory with massless spin-$\frac{5}{2}$ gauge fields. We first introduce the simplest hyper-Maxwell-Chern-Simons gravity generically containing two massless spin-2 fields coupled with a massless Majorana fermion of spin $\frac{5}{2}$ whose novel underlying superalgebra is explicitly constructed. We then present three alternative hypersymmetric extensions of the Maxwell algebra which are shown to emerge from the In\"on\"u-Wigner contraction procedure of precise combinations of the $\mathfrak{o}\mathfrak{s}\mathfrak{p}(1|4)$ and the $\mathfrak{s}\mathfrak{p}(4)$ algebras. This allows us to construct distinct types of hyper-Maxwell-Chern-Simons theories that extend to include generically interacting nonpropagating spin-4 fields accompanied by one or two spin-$\frac{5}{2}$ gauge fields.

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Citations
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TL;DR: The conformal symmetry algebra in 2D (Diff(S1)⊕Diff (S1)) is shown to be related to its ultra/non-relativistic version (BMS3≈GCA2) through a nonlinear map of the generators, without any sort of limiting process.
Abstract: The conformal symmetry algebra in 2D (Diff(S1)⊕Diff(S1)) is shown to be related to its ultra/non-relativistic version (BMS3≈GCA2) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT2, the BMS3 generators then emerge as composites built out from the chiral (holomorphic) components of the stress-energy tensor, T and $$ \overline{T} $$ , closing in the Poisson brackets at equal time slices. Nevertheless, supertranslation generators do not span Noetherian symmetries. BMS3 becomes a bona fide symmetry once the CFT2 is marginally deformed by the addition of a $$ \sqrt{T\overline{T}} $$ term to the Hamiltonian. The generic deformed theory is manifestly invariant under diffeomorphisms and local scalings, but it is no longer a CFT2 because its energy and momentum densities fulfill the BMS3 algebra. The deformation can also be described through the original CFT2 on a curved metric whose Beltrami differentials are determined by the variation of the deformed Hamiltonian with respect to T and $$ \overline{T} $$ . BMS3 symmetries then arise from deformed conformal Killing equations, corresponding to diffeomorphisms that preserve the deformed metric and stress-energy tensor up to local scalings. As an example, we briefly address the deformation of N free bosons, which coincides with ultra-relativistic limits only for N = 1. Furthermore, Cardy formula and the S-modular transformation of the torus become mapped to their corresponding BMS3 (or flat) versions.

17 citations

Journal ArticleDOI
TL;DR: In this article , a spin-3 extension of the AdS algebra was obtained by applying the expansion procedure using different semigroups, leading to spin 3 extensions of known non-relativistic and ultra-relateivistic algebras.
Abstract: In this paper, we present novel and known non-relativistic and ultra-relativistic spin-3 algebras, by considering the Lie algebra expansion method. We start by applying the expansion procedure using different semigroups to the spin-3 extension of the AdS algebra, leading to spin-3 extensions of known non-relativistic and ultra-relativistic algebras. We then generalize the procedure considering an infinite-dimensional semigroup, which allows to obtain a spin-3 extension of two new infinite families of the Newton-Hooke type and AdS-Carroll type. We also present the construction of the gravity theories based on the aforementioned algebras. In particular, the expansion method based on semigroups also allows to derive the (non-degenerate) invariant bilinear forms, ensuring the proper construction of the Chern-Simons gravity actions. Interestingly, in the vanishing cosmological constant limit we recover the spin-3 extensions of the infinite-dimensional Galilean and infinite-dimensional Carroll gravity theories.

4 citations

Journal ArticleDOI
TL;DR: In this article, an extension of the Maxwellian Carroll symmetry is shown to be necessary in order for the invariant tensor of the ultra-relativistic Maxwellian algebra to be non-degenerate.

1 citations

Posted Content
TL;DR: The conformal symmetry algebra in 2D (Diff($S^{1}$)$\oplus$Diff$S€ 1}$)) is shown to be related to its ultra/non-relativistic version (BMS${3}$ ) through a nonlinear map of the generators, without any sort of limiting process as discussed by the authors.
Abstract: The conformal symmetry algebra in 2D (Diff($S^{1}$)$\oplus$Diff($S^{1}$)) is shown to be related to its ultra/non-relativistic version (BMS$_{3}$$\approx$GCA$_{2}$) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT$_{2}$, the BMS$_{3}$ generators then emerge as composites built out from the chiral (holomorphic) components of the stress-energy tensor, $T$ and $\bar{T}$, closing in the Poisson brackets at equal time slices. Nevertheless, supertranslation generators do not span Noetherian symmetries. BMS$_{3}$ becomes a bona fide symmetry once the CFT$_{2}$ is marginally deformed by the addition of a $\sqrt{T\bar{T}}$ term to the Hamiltonian. The generic deformed theory is manifestly invariant under diffeomorphisms and local scalings, but it is no longer a CFT$_{2}$ because its energy and momentum densities fulfill the BMS$_{3}$ algebra. The deformation can also be described through the original CFT$_{2}$ on a curved metric whose Beltrami differentials are determined by the variation of the deformed Hamiltonian with respect to $T$ and $\bar{T}$. BMS$_{3}$ symmetries then arise from deformed conformal Killing equations, corresponding to diffeomorphisms that preserve the deformed metric and stress-energy tensor up to local scalings. As an example, we briefly address the deformation of $\mathrm{N}$ free bosons, which coincides with ultra-relativistic limits only for $\mathrm{N}=1$. Furthermore, Cardy formula and the S-modular transformation of the torus become mapped to their corresponding BMS$_{3}$ (or flat) versions.

1 citations

Posted Content
TL;DR: In this article, an extension of the Maxwellian Carroll symmetry is presented for the invariant tensor of the ultra-relativistic Maxwellian algebra to be non-degenerate.
Abstract: In this work, we present the three-dimensional Maxwell Carroll gravity by considering the ultra-relativistic limit of the Maxwell Chern-Simons gravity theory defined in three spacetime dimensions. We show that an extension of the Maxwellian Carroll symmetry is necessary in order for the invariant tensor of the ultra-relativistic Maxwellian algebra to be non-degenerate. Consequently, we discuss the origin of the aforementioned algebra and theory as a flat limit. We show that the theoretical setup with cosmological constant yielding the extended Maxwellian Carroll Chern-Simons gravity in the vanishing cosmological constant limit is based on an enlarged extended version of the Carroll symmetry. Indeed, the latter exhibits a non-degenerate invariant tensor allowing the proper construction of a Chern-Simons gravity theory which reproduces the extended Maxwellian Carroll gravity in the flat limit.

1 citations

References
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Journal ArticleDOI
TL;DR: In this article, it was shown that the large-N limits of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds.
Abstract: We show that the large-N limits of certainconformal field theories in various dimensions includein their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds. This is shown bytaking some branes in the full M/string theory and thentaking a low-energy limit where the field theory on thebrane decouples from the bulk. We observe that, in this limit, we can still trust thenear-horizon geometry for large N. The enhancedsupersymmetries of the near-horizon geometry correspondto the extra supersymmetry generators present in thesuperconformal group (as opposed to just the super-Poincaregroup). The 't Hooft limit of 3 + 1 N = 4 super-Yang–Mills at the conformal pointis shown to contain strings: they are IIB strings. Weconjecture that compactifications of M/string theory on various anti-de Sitterspacetimes is dual to various conformal field theories.This leads to a new proposal for a definition ofM-theory which could be extended to include fivenoncompact dimensions.

15,567 citations

Journal ArticleDOI
TL;DR: By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels.

2,636 citations

Journal ArticleDOI
TL;DR: In this paper, the (p, q)-type anti-de Sitter supergravity theories associated with the three-dimensional adS supergroups OSp (p|2; R )⊗ OSp(q|2, R ) were constructed.

1,399 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the effects of topological properties on the masses of the gauge fields in three-dimensional space-time, where novel, gauge invariant, P and T odd terms of topology origin give rise to masses for the gauge field.

1,307 citations

Journal ArticleDOI
TL;DR: The purpose of the present note is to investigate, in some generality, in which sense groups can be limiting cases of other groups, and how their representations can be obtained from the representations of the groups of which they appear as limits.
Abstract: Classical mechanics is a limiting case of relativistic mechanics. Hence the group of the former, the Galilei group, must be in some sense a limiting case of the relativistic mechanics’ group, the representations of the former must be limiting cases of the latter’s representations. There are other examples for similar relations between groups. Thus, the inhomogeneous Lorentz group must be, in the same sense, a limiting case of the de Sitter groups. The purpose of the present note is to investigate, in some generality, in which sense groups can be limiting cases of other groups (Section I), and how their representations can be obtained from the representations of the groups of which they appear as limits (Section II). Section III deals briefly with the transition from inhomogeneous Lorentz group to Galilei group. It shows in which way the representation up to a factor of the Galilei group, embodied in the Schrodinger equation, appears as a limit of a representation of the inhomogeneous Lorentz group and also gives the reason why no physical interpretation is possible for the real representations of that group.

1,167 citations