Chern-Simons Supergravity Research Articles

Hietarinta Chern–Simons supergravity and its asymptotic structure

In this paper we present the Hietarinta Chern–Simons supergravity theory in three space-time dimensions which extends the simplest Poincaré supergravity theory. After approaching the construction of the action using the Chern–Simons formalism, the analysis of the corresponding asymptotic symmetry algebra is considered. For this purpose, we first propose a consistent set of asymptotic boundary conditions for the aforementioned supergravity theory whose underlying symmetry corresponds to the supersymmetric extension of the Hietarinta algebra. We then show that the corresponding charge algebra contains the super-bms3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathfrak {bms}}}_{3}$$\\end{document} algebra as subalgebra, and has three independent central charges. We also show that the obtained asymptotic symmetry algebra can alternatively be recovered as a vanishing cosmological constant limit of three copies of the Virasoro algebra, one of which is augmented by supersymmetry.

Formula omitted] resonant superalgebra for supergravity

We present new superalgebra for N=2D=3,4 supergravity theory endowed with the U(1) generator. The superalgebra is rooted in the so-called Soroka-Soroka algebra and spanned by the Lorentz Jab and Lorentz-like Zab, translation Pa and T generators, as well as two supercharges QαI. It is the only possible realization for a given generator content. We construct a corresponding 3D Chern-Simons supergravity realization of the superalgebra and discuss its relevance.

Three-dimensional teleparallel Chern-Simons supergravity theory

In this work we present a gauge-invariant three-dimensional teleparallel supergravity theory using the Chern-Simons formalism. The present construction is based on a supersymmetric extension of a particular deformation of the Poincaré algebra. At the bosonic level the theory describes a non-Riemannian geometry with a non-vanishing torsion. In presence of supersymmetry, the teleparallel supergravity theory is characterized by a non-vanishing super-torsion in which the cosmological constant can be seen as a source for the torsion. We show that the teleparallel supergravity theory presented here reproduces the Poincaré supergravity in the vanishing cosmological limit. The extension of our results to {mathcal {N}}=p+q supersymmetries is also explored.

Non-relativistic three-dimensional supergravity theories and semigroup expansion method

In this work we present an alternative method to construct diverse non-relativistic Chern-Simons supergravity theories in three spacetime dimensions. To this end, we apply the Lie algebra expansion method based on semigroups to a supersymmetric extension of the Nappi-Witten algebra. Two different families of non-relativistic superalgebras are obtained, corresponding to generalizations of the extended Bargmann superalgebra and extended Newton-Hooke superalgebra, respectively. The expansion method considered here allows to obtain known and new non-relativistic supergravity models in a systematic way. In particular, it immediately provides an invariant tensor for the expanded superalgebra, which is essential to construct the corresponding Chern-Simons supergravity action. We show that the extended Bargmann supergravity and its Maxwellian generalization appear as particular subcases of a generalized extended Bargmann supergravity theory. In addition, we demonstrate that the generalized extended Bargmann and generalized extended Newton-Hooke supergravity families are related through a contraction process.

A note on the mathcal{N} = 2 super- {mathcal{W}}_3 holographic dictionary

This is a long-overdue companion paper to [1]. We study the relation between sl(3|2) Chern-Simons supergravity on AdS3 and two-dimensional CFT’s with mathcal{N} = 2 super- {mathcal{W}}_3 symmetry. Specifically, we carry out a complete analysis of asymptotic symmetries in a basis that makes the superconformal structure transparent, allowing us to establish the precise dictionary between currents and transformation parameters in the bulk and their boundary counterparts. We also discuss the incorporation of sources and display in full detail the corresponding holographic Ward identities. By imposing suitable hermiticity conditions on the CFT currents, we identify the superalgebra su(2, 1|1, 1) as the appropriate real form of sl(3|2) in Lorentzian signature. We take the opportunity to review some of the properties of the mathcal{N} = 2 super- {mathcal{W}}_3 conformal algebra, including its multiplet structure, OPE’s and spectral flow invariance, correcting some minor typos present in the literature.

Chern-Simons supergravity on supergroup manifolds

We construct N=1 d=3 AdS supergravity within the group manifold approach and compare it with Achucarro-Townsend Chern-Simons formulation of the same theory. We clarify the relation between the off-shell super gauge transformations of the Chern- Simons theory and the off-shell worldvolume supersymmetry transformations of the group manifold action. We formulate the Achucarro-Townsend model in a double supersymmetric action where the Chern-Simons theory with a supergroup gauge symmetry is constructed on a supergroup manifold. This framework is useful to establish a correspondence of degrees of freedom and auxiliary fields between the two descriptions of d=3 supergravity.

Three-dimensional Maxwellian extended Bargmann supergravity

We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra. We first study the non-relativistic limits of the minimal and the mathcal{N} = 2 Maxwell superalgebras. We show that a well-defined Maxwellian extended Bargmann supergravity requires to construct by hand a supersymmetric extension of the Maxwellian extended Bargmann algebra by introducing additional fermionic and bosonic generators. The new non-relativistic supergravity action presented here contains the extended Bargmann supergravity as a sub-case.

Mathcal{N} -extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions

In this work we present the ultra-relativistic mathcal{N} -extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under mathcal{N} -extended AdS Carroll superalgebras. We first consider the (2, 0) and (1, 1) cases; subsequently, we generalize our analysis to mathcal{N} = ( mathcal{N} , 0), with mathcal{N} even, and to mathcal{N} = (p, q), with p, q > 0. The mathcal{N} -extended AdS Carroll superalgebras are obtained through the Carrollian (i.e., ultra-relativistic) contraction applied to an so(2) extension of mathfrak{osp} (2|2) ⊗ mathfrak{sp} (2), to mathfrak{osp} (2|1) ⊗ mathfrak{osp} (2, 1), to an mathfrak{so}left(mathcal{N}right) extension of mathfrak{osp} (2| mathcal{N} ) ⊗ mathfrak{sp} (2), and to the direct sum of an mathfrak{so} (p) ⊕ mathfrak{so} (q) algebra and mathfrak{osp} (2|p) ⊗ mathfrak{osp} (2, q), respectively. We also analyze the flat limit (ℓ → ∞, being ℓ the length parameter) of the aforementioned mathcal{N} -extended Chern-Simons AdS Carroll supergravities, in which we recover the ultra-relativistic mathcal{N} -extended (flat) Chern-Simons supergravity theories invariant under mathcal{N} -extended super-Carroll algebras. The flat limit is applied at the level of the superalgebras, Chern-Simons actions, supersymmetry transformation laws, and field equations.

Different Approaches to Unveil Biomolecule Configurations and Their Mutual Interactions

A novel technique was demonstrated that overcomes important drawbacks to crosslink cells by irradiation with ultrashort ultraviolet laser pulses (L-crosslinking). To use this technique coupled to Chromatin ImmunoPrecipitation (ChIP) in a high throughput context, a prescreening fast method needs to be implemented to set up suitable irradiation conditions of the cell sample for efficient L-crosslinking with no final and long ChIP analysis. Here a fast method is reported where living human cells have been first transfected with a vector coding for Estrogen Receptor α (ERα), linked to Green Florescent protein (ERα-GFP), so that the well-known interaction between the Estrogen Receptor Elements (ERE) region of the cell DNA and the ERα protein can be detected by studying the fluorometric response of the irradiated cells. The damage induced to cells by ultraviolet irradiation is characterized by looking at the DNA integrity, protein stability, and cellular viability. A second novel approach is presented to analyze or re-visit DNA and RNA sequences and their molecular configurations. This approach is based on methods derived from Chern-Simons super-gravity adapted to describe mutations in DNA/RNA strings, as well as interactions between nucleic acids. As a preliminary case, we analyze the KRAS human gene sequence and some of its mutations. Interestingly, our model shows how the Chern-Simons currents are able to characterize the mutations within a sequence, in particular giving a quantitative indication of the mutation likelihood.

Three-dimensional extended Lifshitz, Schrödinger and Newton-Hooke supergravity

We provide a systematic analysis of three-dimensional mathcal{N} = 2 extended Bargmann superalgebra and its Newton-Hooke, Lifshitz and Schrödinger extensions. These algebras admit invariant non-degenerate bi-linear forms which we utilized to construct corresponding Chern-Simons supergravity actions.

Extended D = 3 Bargmann supergravity from a Lie algebra expansion

In this paper we show how the method of Lie algebra expansions may be used to obtain, in a simple way, both the extended Bargmann Lie superalgebra and the Chern-Simons action associated to it in three dimensions, starting from D=3, N=2 superPoincaré and its corresponding Chern-Simons supergravity.

AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit

Carroll symmetries arise when the velocity of light is sent to zero (ultra-relativistic limit). In this paper, we present the construction of the three-dimensional Chern-Simons supergravity theory invariant under the so-called AdS Carroll superalgebra, which was obtained in the literature as a contraction of the AdS superalgebra. The action is characterized by two coupling constants. Subsequently, we study its flat limit, obtaining the three-dimensional Chern-Simons supergravity theory invariant under the super-Carroll algebra, which is a contraction of the Poincaré superalgebra. We apply the flat limit at the level of the superalgebra, Chern-Simons action, supersymmetry transformation laws, and field equations.

The quantum theory of Chern-Simons supergravity

We consider AdS3N-extended Chern-Simons supergravity (à la Achucarro-Townsend) and we study its gauge symmetries. We promote those gauge symmetries to a BRST symmetry and we perform its quantization by choosing suitable gauge-fixings. The resulting quantum theories have different features which we discuss in the present work. In particular, we show that a special choice of the gauge-fixing correctly reproduces the Ansatz by Alvarez, Valenzuela and Zanelli for the graphene fermion.

Three-dimensional Poincaré supergravity and [formula omitted]-extended supersymmetric BMS3 algebra

A new approach for obtaining the three-dimensional Chern-Simons supergravity for the Poincaré algebra is presented. The N-extended Poincaré supergravity is obtained by expanding the super Lorentz theory. We extend our procedure to their respective asymptotic symmetries and show that the N=(1,2,4) super-BMS3 appear as expansions of one Virasoro superalgebra. Interestingly, the N-extended super-BMS3 obtained here are not only centrally extended but also endowed with internal symmetry. We also show that the N-extended super Poincaré algebras with both central and automorphism generators are finite subalgebras.

Minimal AdS-Lorentz supergravity in three-dimensions

The N=1 AdS-Lorentz superalgebra is studied and its relationship to semigroup expansion developed. Using this mathematical tool, the invariant tensors and Casimir operators are found. In terms of these invariants, a three-dimensional Chern–Simons supergravity action with AdS-Lorentz symmetry is constructed. The Killing spinors for a BTZ black-hole like solution of the theory are discussed.

On the Maxwell supergravity and flat limit in 2 + 1 dimensions

The construction of the three-dimensional Chern–Simons supergravity theory invariant under the minimal Maxwell superalgebra is presented. We obtain a supergravity action without cosmological constant term characterized by three coupling constants. We also show that the Maxwell supergravity presented here appears as a vanishing cosmological constant limit of a minimal AdS–Lorentz supergravity. The flat limit is applied at the level of the superalgebra, Chern–Simons action, supersymmetry transformation laws and field equations.

Chern–Simons supergravity in [formula omitted] and Maxwell superalgebra

We present the construction of the D=3 Chern–Simons supergravity action without cosmological constant from the minimal Maxwell superalgebra sM3. This superalgebra contains two Majorana fermionic charges and can be obtained from the osp(2|1)⊗sp(2) superalgebra using the abelian semigroup expansion procedure. The components of the Maxwell invariant tensor are explicitly derived.

Black hole solutions in Chern-Simons AdS supergravity

We study charged AdS black hole solutions in five-dimensional Chern-Simons supergravity. The minimal supergroup containing such AdSxU(1) configurations is the superunitary group SU(2,2|N). For this model, we find analytic black hole solutions that asymptote to locally AdS spacetime at the boundary. A solution can carry U(1) charge provided the spacetime torsion is non-vanishing. Thus, we analyze the most general configuration consistent with the local AdS isometries in Riemann-Cartan space. The coupling of torsion in the action resembles that of the universal axion of string theory, and it is ultimately due to this field that the theory acquires propagating degrees of freedom. Through a careful analysis of the canonical structure the local degrees of freedom of the theory are identified in the static symmetric sector of phase space.

Covariant quiver gauge theories

We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver bundles, and show that the reduced quiver gauge theories are all generically built on the same universal symmetry breaking pattern. The formalism enables the dimensional reduction of Chern-Simons gauge theories in arbitrary odd dimensionalities. The reduced model is a novel Chern-Simons-Higgs theory consisting of a Chern-Simons term valued in the residual gauge group plus a higher order gauge and diffeomorphism invariant coupling of Higgs fields with the gauge fields. We study the moduli spaces of solutions, which in some instances provide geometric representations of certain quiver varieties as moduli spaces of flat invariant connections. As physical applications, we consider dimensional reductions involving non-compact gauge supergroups as a means for systematically inducing novel couplings between gravity and matter. In particular, we reduce Chern-Simons supergravity to a quiver gauge theory of AdS gravity involving a non-minimal coupling to scalar Higgs fermion fields.

Chern-Simons supergravities, with a twist

We discuss noncommutative extensions of Chern-Simons (CS) supergravities in odd dimensions. The example of D = 5 CS supergravity, invariant under the gauge supergroup SU(2, 2|N), is worked out in detail. Its noncommutative version, with a ⋆-product associated to an abelian Drinfeld twist, is found to exist only for N = 4.