A superconnection formalism for gauge theories of gravity

Belarbi, Oussama A.; Meziane, Ahmed

doi:10.1063/5.0163338

Cited by 1 publication

(2 citation statements)

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“…To recapitulate, by dint of the superspace formalism [47] with a GA(4, R)superconnection ϕ and its associated supercurvature Ω, we have identified all the necessary fields for a topological gauge-affine gravity. The direct method used here consists in defining a new basis (b M ) instead of the usual one (dZ M ) in order to incorporate the diffeomorphism ghost.…”

Section: Discussionmentioning

confidence: 99%

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In Pursuit of BRST Symmetry and Observables in 4D Topological Gauge-Affine Gravity

Belarbi,

Meziane

2024

Symmetry

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The realization of a BRST cohomology of the 4D topological gauge-affine gravity is established in terms of a superconnection formalism. The identification of fields in the quantized theory occurs directly as is usual in terms of superconnection and its supercurvature components with the double covering of the general affine group GA¯(4,R). Then, by means of an appropriate decomposition of the metalinear double-covering group SL¯(5,R) with respect to the general linear double-covering group GL¯(4,R), one can easily obtain the enlargements of the fields while remaining consistent with the BRST algebra. This leads to the descent equations, allowing us to build the observables of the theory by means of the BRST algebra constructed using a sa¯(5,R) algebra-valued superconnection. In particular, we discuss the construction of topological invariants with torsion.

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Section: Discussionmentioning

confidence: 99%

“…Moreover, as a formalism, we chose to use the superconnection formalism; cf. [47]. Our paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%