Comments on Gluino Condensates in N=1/2 SYM Theory

TL;DR

This paper investigates how certain gluino condensates in N=1/2 supersymmetric Yang-Mills theory are affected by C-deformation, revealing invariance in some quantities and explicit dependence in others through Ward identities.

Contribution

It demonstrates the invariance of the partition function and antichiral gluino condensates under C-deformation and derives the dependence of chiral gluino correlators on the deformation parameter.

Findings

Partition function remains invariant under C-deformation.

Antichiral gluino condensates are unaffected by C-deformation.

Chiral gluino correlators depend explicitly on the deformation parameter.

Abstract

Using Ward identities of N=1/2 supersymmetric Yang-Mills theory, we show that while the partition function and antichiral gluino condensates remain invariant under the $C$ deformation, chiral gluino correlators can get contributions from all gauge fields with instanton numbers $k\leq 1$. In particular, a Ward identity of the $U(1)_R$ symmetry allows us to determine the explicit dependence of chiral gluino correlators on the deformation parameter.