TL;DR
This paper explores the geometric foundations of BRST and anti-BRST symmetries in gauge theories, linking algebraic properties to bundle and gerbe geometries, and clarifying conditions like Curci-Ferrari constraints.
Contribution
It provides a geometric interpretation of BRST and anti-BRST symmetries and the Curci-Ferrari conditions within the framework of bundles and gerbes, extending to higher-form gauge fields.
Findings
Geometric interpretation of Curci-Ferrari conditions.
Explicit construction of 3-form gauge fields.
Comparison of gauge field geometries with algebraic symmetries.
Abstract
We continue the comparison between the field theoretical and geometrical approaches to the gauge field theories of various types, by deriving their Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST trasformation properties and comparing them with the geometrical properties of the bundles and gerbes. In particular, we provide the geometrical interpretation of the so--called Curci-Ferrari conditions that are invoked for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations in the context of non-Abelian 1-form gauge theories as well as Abelian gauge theory that incorporates a 2-form gauge field. We also carry out the explicit construction of the 3-form gauge fields and compare it with the geometry of 2--gerbes.
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