Geometrical Formulation of the BRST Transformations of Gauge-Affine Gravity

Abstract

Fields and their BRST and anti-BRST transformations in gauge-affine gravity are determined by using a superspace formalism. The method is based on the introduction of a basis, instead of the natural one, for differential forms on a (4, 2)-dimensional superspace, whose body is a metric-affine spacetime. This basis is defined after having introduced the coordinate ghost and anti-ghost superfields from a [Formula: see text]-superconnection.

Quantized gauge-affine gravity in the superfiber bundle approach

“…Then the supercurvature constraints are determined by the fact that the generalized supercurvature is an even tensorial 2-superform which leads to the determination of the gauge-affine gravity BRST and anti-BRST transformations. The obtained BRST transformations are nilpotent and equivalent to those given in [18,20,25]. Reducing the four-dimensional general affine group double-covering GA(4, R) to the Poincaré group double-covering ISO(1, 3) we have also found the BRST and anti-BRST transformations of the fields present in quantum Einstein gravity.…”

“…Indeed, as shown in Ref. [25], we have used a superspace formalism to determine geometrically the BRST and anti-BRST algebra for gauge-affine gravity. Our method was based on the introduction of GA(4, R)-superconnection over a (4, 2)-dimensional superspace obtained by extending a metric-affine space with two anticommuting coordinates.…”

A superconnection formalism for gauge theories of gravity

“…Here, we should stress that BRST and anti-BRST transformations of such a model were found earlier by the authors of [16]. Accordingly, we will follow the same path and construct new observables for a gauge-affine gravity [17], knowing that BRST and anti-BRST transformations of this model based on the gauge group A(4, R) were found first in [9]. (For a review on topological obervables in topological gravity see [18])…”

“…where m = 0 if N = µ and m = 1 if N = α. We denote the ghost number of a field by gh(), such that gh(θ 1 ) = −1, gh(θ 2 ) = 1 and the ghost number of all fields with even-parity vanishes, namely [9] gh(φ ab µ , φ a µ , φ ab…”

“…(For an exhaustive and self-contained review on metric-affine theory based on gauge principle, see [2] and references therein) For this purpose, a plenty of mathematical models and formalisms have been developed in order to deal with the problem of quantization of gauge theories and in particular of gauge theories of gravity; a superconnection formalism is one of them. In the program of attempting to quantize gauge theories of gravity, BRST and anti-BRST algebra of a gauge-affine gravity [7,8] was obtained geometrically using a superconnection formalism [9].…”