Dirac matrices for Chern-Simons gravity

Izaurieta, Fernando; Ramírez, Ricardo; Rodríguez, Evelyn

doi:10.1063/1.4756824

Cited by 5 publications

(9 citation statements)

References 23 publications

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“…Let us assume a three-dimensional manifold whose local geometry is of the form   Σ = × , where  represents the time direction and Σ is the two-dimensional spatial section. As shown in [34,35,39], the regularized CS action is given by the transgression form  , defined as…”

Section: Transgression Action and Chargesmentioning

confidence: 99%

Supersymmetric 3D model for gravity with SU (2) gauge symmetry, mass generation and effective cosmological constant

Alvarez

Pais

Rodríguez

et al. 2015

Class. Quantum Grav.

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A Chern-Simons system in 2 + 1 dimensions invariant under local Lorentz rotations, SU (2) gauge transformations, and local N = 2 supersymmetry transformations is proposed. The field content is that of (2 + 1)-gravity plus an SU (2) gauge field, a spin-1/2 fermion charged with respect to SU (2) and a trivial free abelian gauge field. A peculiarity of the model is the absence of gravitini, although it includes gravity and supersymmetry. Likewise, no gauginos are present. All the parameters involved in the system are either protected by gauge invariance or emerge as integration constants. An effective mass and effective cosmological constant emerge by spontaneus breaking of local scaling invariance. The vacuum sector is defined by configurations with locally flat Lorentz and SU (2) connections sporting nontrivial global charges. Three-dimensional Lorentz-flat geometries are spacetimes of locally constant negative -or zero-, Riemann curvature, which include Minkowski space, AdS3, BTZ black holes, and point particles. These solutions admit different numbers of globally defined, covariantly constant spinors and are therefore good candidates for stable ground states. The fermionic sector in this system could describe the dynamics of electrons in graphene in the long wavelength limit near the Dirac points, with the spin degree of freedom of the electrons represented by the SU (2) label. If this is the case, the SU (2) gauge field would produce a spin-spin interaction giving rise to strong correlation of electron pairs. A. Representation of the su(2, 1|2) superalgebra 12 B. Killing spinors 13 1. Case M = W = −1; J = K = 0 13 2. Case M = J = W = K = 0 13 3. Case M, W > 0; M = |J|/l, W = |K|/y 14 References 14

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Section: Transgression Action and Chargesmentioning

confidence: 99%

Supersymmetric 3D model for gravity with SU (2) gauge symmetry, mass generation and effective cosmological constant

Alvarez

Pais

Rodríguez

et al. 2015

Class. Quantum Grav.

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“…With those transformations defined, it is possible to write down a gauge invariant theory. The definition of transgression and CS forms for FDA1 can be found by studying the corresponding Chern-Weil theorem [34,40,41]. Let A = A A , A i be a set of gauge fields composed by a one-form and a p-form.…”

Section: Jhep04(2022)142mentioning

confidence: 99%

On the L∞ formulation of Chern-Simons theories

Salgado

2022

J. High Energ. Phys.

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L∞ algebras have been largely studied as algebraic frameworks in the formulation of gauge theories in which the gauge symmetries and the dynamics of the interacting theories are contained in a set of products acting on a graded vector space. On the other hand, FDAs are differential algebras that generalize Lie algebras by including higher-degree differential forms in their differential equations. In this article, we review the dual relation between FDAs and L∞ algebras. We study the formulation of standard Chern-Simons theories in terms of L∞ algebras and extend the results to FDA-based gauge theories. We focus on two cases, namely a flat (or zero-curvature) theory and a generalized Chern-Simons theory, both including high-degree differential forms as fundamental fields.

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“…From Ref. [18] we find that the non-vanishing components of the invariant tensor for so(4, 2) are given by…”

Section: Gb N Algebrasmentioning

confidence: 99%

Generalized Galilean algebras and Newtonian gravity

et al. 2016

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The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. This non-relativistic algebras are called, generalized Galilean algebras type I and type II and denoted by GB n and GL n respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB 5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref.[1] allow us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

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Dirac matrices for Chern-Simons gravity

Cited by 5 publications

References 23 publications

Supersymmetric 3D model for gravity with SU (2) gauge symmetry, mass generation and effective cosmological constant

Supersymmetric 3D model for gravity with SU (2) gauge symmetry, mass generation and effective cosmological constant

On the L∞ formulation of Chern-Simons theories

Generalized Galilean algebras and Newtonian gravity

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