Renormalizability of the center-vortex free sector of Yang-Mills theory

Abstract

In this work, we analyze a recent proposal to detect SUðNÞ continuum Yang-Mills sectors labeled by center vortices, inspired by Laplacian-type center gauges in the lattice. Initially, after the introduction of appropriate external sources, we obtain a rich set of sector-dependent Ward identities, which can be used to control the form of the divergences. Next, we show the all-order multiplicative renormalizability of the center-vortex free sector. These are important steps towards the establishment of a first-principles, well-defined, and calculable Yang-Mills ensemble.

From Center-Vortex Ensembles to the Confining Flux Tube

“…In [51], the gauge was locally fixed by a regular gauge transformation that rotates S to the reference S 0 , which is imposed by a sector dependent condition f S 0 (ψ) = 0. Furthermore, the theory was shown to be renormalizable in the vortex-free sector [54]. The extension of the renormalization proof to sectors labeled by center vortices is under way, and will be presented elsewhere.…”

Renormalizability of center-vortex sectors in continuum Yang-Mills theory

“…In Ref. [13], we established the renormalizability of the vortex-free sector by using the algebraic method, and then, in Ref. [14], this was generalized to a sector containing an arbitrary number of elementary center vortices.…”

“…This was firstly studied for the vortex-free sector in Ref. [13], and then generalized to a sector containing a general oriented elementary center-vortex configuration in Ref. [14].…”

Renormalizability of a first principles Yang-Mills center-vortex ensemble

“…In Ref. [26], relying on the algebraic method, we showed that this property is valid in the vortex-free sector (S 0 = I), where the possible counter-terms are restricted by the Ward Identities of the gauge-fixed action. In this work, we present a proof of renormalizability for the center-vortex sectors.…”

“…with the covariant derivative defined as D ab µ = δ ab ∂ µ − gf abc A c µ . To fix the gauge in the vortex-free sector, we follow the procedure developed in [13,26]. The first step is to introduce a set of auxiliary fields ζ a I , b a I , c a I , ca I , where the flavor index takes values in {1, 2, .…”