BV-BRST Noether theorem
Glenn Barnich, Laurent Baulieu, Marc Henneaux, Tom Wetzstein
TL;DR
The paper proves the BRST Noether current is BRST-trivial up to a total divergence, extending Noether 1.5 to general gauge theories without restricting the antifield structure. It delivers two independent proofs: one via gauge-fixed Noether analysis and another through a gauge-independent BRST master current in the antifield (BV–BRST) framework, using homological perturbation theory. A central result is the explicit relation j^μ_s = - s j_G^μ + ∂_ν k^{[μν]}_s between the BRST master current and the ghost-number current, which, upon gauge fixing, reduces to the Noether 1.5 relation j^μ_{γ^g} ≈ - γ^g j^g_G + ∂ k. The work clarifies the structural link between Noether currents, BRST symmetry, and the master equation, with implications for asymptotic symmetries and future quantum analyses via Ward identities.
Abstract
The BRST Noether theorem, or ``Noether's 1.5 theorem'', asserts the triviality of the BRST Noether current. We provide two proofs of this theorem that are both valid without restriction on the structure of the gauge theory, extending thereby previous proofs holding in the case of gauge theories for which the solution of the master equation is linear in the antifields. We also relate explicitly the BRST Noether current to the BRST master current appearing in the master equation.