Analyzing Chiral Symmetry Breaking in Supersymmetric Gauge Theories

TL;DR

This paper compares gap equation predictions with nonperturbative techniques for chiral symmetry breaking in supersymmetric gauge theories, highlighting agreements and discrepancies in the formation of condensates and symmetry breaking.

Contribution

It provides a comparative analysis of gap equations and holomorphic effective action methods in supersymmetric theories, exploring their predictions for symmetry breaking and condensate formation.

Findings

Both approaches agree on gluino condensate formation in pure Yang-Mills.

For theories with flavors, gap equations predict symmetry breaking solutions.

Discrepancies exist between gap equations and nonperturbative results for flavored theories.

Abstract

We compare gap equation predictions for the spontaneous breaking of global symmetries in supersymmetric Yang-Mills theory to nonperturbative results from holomorphic effective action techniques. In the theory without matter fields, both approaches describe the formation of a gluino condensate. With $N_f$ flavors of quark and squark fields, and with $N_f$ below a certain critical value, the coupled gap equations have a solution for quark and gluino condensate formation, corresponding to breaking of global symmetries and of supersymmetry. This appears to disagree with the newer nonperturbative techniques, but the reliability of gap equations in this context and whether the solution represents the ground state remain unclear.