# Large-N Wilsonian beta function in SUN Yang-Mills theory by localization on the fixed points of a semigroup contracting the functional measure - High Energy Physics - Theory

Large-N Wilsonian beta function in SUN Yang-Mills theory by localization on the fixed points of a semigroup contracting the functional measure - High Energy Physics - Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: In a certain non-commutative version of large-N SUN Yang-Mills theorythere are special Wilson loops, called twistor Wilson loops for geometricalreasons, whose v.e.v. is independent on the parameter that occurs in theiroperator definition. There is a semigroup that acts on the parameter byrescaling and on the functional measure, resolved into anti-selfdual orbits bya non-supersymmetric version of the Nicolai map, by contracting the support ofthe measure. As a consequence the twistor Wilson loops are localized on thefixed points of the semigroup of contractions. This localization is anon-supersymmetric analogue of the localization that occurs in the Nekrasovpartition function of the n=2 SUSY YM theory on the fixed points of a certaintorus action on the moduli space of non-commutative instantons. One mainconsequence of the localization in the large-N YM case, as in the n=2 SUSY YMcase, is that the beta function of the Wilsonian coupling constant in theanti-selfdual variables is one-loop exact. Consequently the large-N Yang-Millscanonical beta function has a NSVZ form that reproduces the first two universalperturbative coefficients.

Author: ** Marco Bochicchio**

Source: https://arxiv.org/