antiBRST

AntiBRST, or anti-BRST, refers to a symmetry that accompanies the BRST symmetry in the quantization of gauge theories. It is a fermionic, global symmetry generated by an anti-BRST operator that acts on the fields of the gauge theory, including the gauge field, ghost, anti-ghost, and auxiliary fields, in a way that mirrors the standard BRST transformations. The anti-BRST symmetry is a structural feature of the gauge-fixing sector and is used to organize and constrain the quantum theory.

In many formulations, the BRST and anti-BRST transformations are required to anticommute and to be nilpotent, with s^2 = 0 and (s̄)^2 = 0, and, under suitable conditions, {s, s̄} = 0. This algebraic structure is most transparent in BRST-anti-BRST symmetric quantization, sometimes referred to as an N=2 BRST framework. In such approaches, the gauge-fixing term is constructed to be invariant under both BRST and anti-BRST transformations, leading to additional identities and consistency conditions.

The anti-BRST symmetry is not a separate physical degree of freedom but rather a complementary symmetry of the gauge-fixed action. It is especially relevant in discussions of gauge independence, renormalizability, and cohomological methods in gauge theories. Anti-BRST is commonly studied in Yang–Mills theories and in certain topological field theories, where the dual structure with BRST helps illuminate the underlying geometry and algebra of the gauge-fixing sector.