$\chi\rm{SB}$ of cascading gauge theory in de Sitter

TL;DR

This paper investigates how chiral symmetry breaking in a specific supersymmetric cascading gauge theory depends on the Hubble constant in de Sitter space, revealing critical thresholds for symmetry breaking.

Contribution

It provides a detailed analysis of chiral symmetry breaking in cascading gauge theories within de Sitter space, identifying specific Hubble constant ranges where symmetry is broken.

Findings

Chiral symmetry breaks for Hubble constant H less than approximately 0.7 times the strong coupling scale Λ.

A narrow window exists where chiral symmetry also breaks, between about 0.92Λ and 0.92(5)Λ.

Defines the strong coupling scale Λ in terms of glueball mass and string coupling.

Abstract

${\cal N}=1$ supersymmetric $SU(N)\times SU(N+M)$ cascading gauge theory of Klebanov et.al spontaneously breaks chiral symmetry in Minkowski space-time. We demonstrate that in de Sitter space-time the chiral symmetry breaking occurs for the values of the Hubble constant $H\lesssim 0.7 \Lambda $, as well as in a narrow window $0.92(1) \Lambda \le H\le 0.92(5) \Lambda $. We give a precise definition of the strong coupling scale $\Lambda $ of cascading gauge theory, which is related to the glueball mass scale in the theory $m_{glueball}$ and the asymptotic string coupling $g_s$ as $\Lambda \sim g_s^{1/2} m_{glueball}$.