Calculating Gluino Condensates in $\mathcal{N}=1$ SYM from Seiberg-Witten Curves

TL;DR

This paper calculates the gluino condensate in various pure  super Yang-Mills theories by deforming  theories with mass, confirming results with weak coupling instanton calculations.

Contribution

It introduces a method to determine gluino condensates in  SYM for different gauge groups using deformations of  theories and Seiberg-Witten curves.

Findings

Gluino condensate values match weak coupling instanton results.

Method applies to multiple gauge groups including SU, SO, and USp.

Confirms consistency of different computational approaches.

Abstract

We determine the gluino condensate $< \Tr \lambda^2 >$ in the pure ${\cal N}=1$ super Yang-Mills theory (SYM) for the classical gauge groups $SU(r+1)$, $SO(2r+1)$, $USp(2r)$ and $SO(2r)$, by deforming the pure ${\cal N}=2$ SYM theory with the adjoint scalar multiplet mass, following the work by Finnell and Pouliot, and Ritz and Vainshtein. The value of the gluino condensate agrees in all cases with what was found in the weak coupling istanton calculation.