Dynamics of Nonintegrable Phases in Softly Broken Supersymmetric Gauge Theory with Massless Adjoint Matter

TL;DR

This paper investigates the behavior of nonintegrable phases in a softly broken supersymmetric gauge theory with massless adjoint matter on a compactified space, revealing how quantum corrections generate a finite Higgs mass.

Contribution

It demonstrates that the gauge symmetry is maximally broken to Abelian factors regardless of flavor number or boundary conditions, and shows how quantum effects induce a finite Higgs mass.

Findings

Gauge symmetry breaks to U(1)^{N-1} regardless of boundary conditions.

Quantum corrections produce a finite Higgs mass in small extra dimensions.

Supersymmetry breaking via Scherk-Schwarz mechanism influences Higgs mass generation.

Abstract

We study SU(N) supersymmetric Yang-Mills theory with massless adjoint matter defined on $M^3\otimes S^1$. The SU(N) gauge symmetry is broken maximally to $U(1)^{N-1}$, independent of the number of flavor and the boundary conditions of the fields associated with the Scherk-Schwarz mechanism of supersymmetry breaking. The mass of the Higgs scalar is generated through quantum corrections in the extra dimensions. The quantum correction can become manifest by a finite Higgs boson mass at low energies even in the limit of small extra dimensions thanks to the supersymmetry breaking parameter of the Scherk-Schwarz mechanism.