# On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials - High Energy Physics - Theory

On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials - High Energy Physics - Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: We study the algebraic and geometric structures that underly the space ofvacua of N=1 super Yang-Mills theories at the non-perturbative level. Chiraloperators are shown to satisfy polynomial equations over appropriate rings, andthe phase structure of the theory can be elegantly described by thefactorization of these polynomials into irreducible pieces. In particular, thisidea yields a powerful method to analyse the possible smooth interpolationsbetween different classical limits in the gauge theory. As an application inUNc theories, we provide a simple and completely general proof of the factthat confining and Higgs vacua are in the same phase when fundamental flavorsare present, by finding an irreducible polynomial equation satisfied by theglueball operator. We also derive the full phase diagram for the theory withone adjoint when Nc is less than or equal to 7 using computational algebraicgeometry programs.

Author: ** Frank Ferrari**

Source: https://arxiv.org/