BRS symmetry from renormalization group flow

Abstract

By using the exact renormalization group formulation we prove perturbatively the Slavnov-Taylor (ST) identities in SU(2) Yang-Mills theory. This results from two properties: {\it locality}, i.e. the ST identities are valid if their local part is valid; {\it solvability}, i.e. the local part of ST identities is valid if the couplings of the effective action with non-negative dimensions are properly chosen.Comment: 9 pages, LaTex, to be published in Phys. Lett.

Background field method in the Wilson formulation

“…This analysis can be performed as in the standard Wilsonian approach for gauge theories [2,3]. First one introduces a cutoff dependent BRS transformation, studies the modified ST identities and determines the non-invariant couplings which compensate the breaking introduced by the cutoff.…”

Wilson renormalization group for supersymmetric gauge theories and gauge anomalies

“…Despite the presence of the cutoff Λ which explicitly breaks gauge invariance, one proves that, by properly fixing the boundary conditions of the RG equation, the Slavnov-Taylor (ST) identity can be satisfied when all cutoffs are removed (at least in perturbation theory). This has been shown for the pure Yang-Mills case both in terms of the "bare" couplings of the effective action at the ultraviolet scale [7] and of the physical couplings [10]. Furthermore, as this method directly works in four space-time dimensions, it naturally extends [12] to chiral gauge theories with no ambiguity in the definition of the matrix γ 5 (contrary to dimensional regularization).…”

“…Recently a regularization procedure based on the Wilson renormalization group (RG) has been formulated [6,7] for scalar field theories [8,9] and gauge theories [7,10,11]. With this method one introduces an ultraviolet (UV) and infrared (IR) cutoff, Λ and Λ 0 respectively, in the propagator so that all Feynman diagrams become convergent in the UV region.…”

Beta function and flowing couplings in the exact Wilson renormalization group in Yang-Mills theory

“…We recall that the Λ-RG for this theory is consistent with the BRS symmetry [14] provided the boundary conditions at the physical point Λ = 0 and Λ → ∞ are properly chosen [4,6] (see also [15]). We then consider the iterative solution in terms of the Wilsonian couplings.…”

“…It is interesting to observe that in the Yang-Mills case the UV action in general does not satisfy the BRS symmetry and then it could be surprising that the beta function is given in terms of the UV parameters. However one should observe that these UV parameters depend on g and µ/Λ 0 in such a way that the physical effective action (Λ = 0 and Λ 0 → ∞) satisfies Slavnov-Taylor identities [4,6].…”