Generalized gaugings and the field-antifield formalism

TL;DR

This paper explores the algebraic structure of general gauge theories using the embedding tensor formalism and links it to the field-antifield (BV) formalism, highlighting the connection through the master equation.

Contribution

It demonstrates how the embedding tensor formalism integrates into the field-antifield formalism, revealing the algebraic complexity and reducibility of gauge transformations.

Findings

Embedding tensor formalism fits into the BV master equation.

Gauge transformations can be infinitely reducible.

Connection clarifies quantization of general gauge theories.

Abstract

We discuss the algebra of general gauge theories that are described by the embedding tensor formalism. We compare the gauge transformations dependent and independent of an invariant action, and argue that the generic transformations lead to an infinitely reducible algebra. We connect the embedding tensor formalism to the field-antifield (or Batalin-Vilkovisky) formalism, which is the most general formulation known for general gauge theories and their quantization. The structure equations of the embedding tensor formalism are included in the master equation of the field-antifield formalism.