On Instantons and Zero Modes of N=1/2 SYM Theory

TL;DR

This paper investigates zero modes in N=1/2 supersymmetric Yang-Mills theory with instantons, revealing how fermionic solutions affect the action's minimization and the structure of instanton solutions.

Contribution

It introduces deformed instanton equations accounting for fermionic solutions, showing how these solutions alter the action's minimization and the nature of instantons in N=1/2 SYM.

Findings

Fermionic solutions are not always zero modes of the action due to a quartic fermionic term.

Deformed instanton equations incorporate fermionic solutions, satisfying equations of motion and saturating the BPS bound.

Finite action solutions involve non-flat U(1) connections, indicating a modified instanton structure.

Abstract

We study zero modes of N=1/2 supersymmetric Yang-Mills action in the background of instantons. In this background, because of a quartic antichiral fermionic term in the action, the fermionic solutions of the equations of motion are not in general zero modes of the action. Hence, when there are fermionic solutions, the action is no longer minimized by instantons. By deforming the instanton equation in the presence of fermions, we write down the zero mode equations. The solutions satisfy the equations of motion, and saturate the BPS bound. The deformed instanton equations imply that the finite action solutions have U(1) connections which are not flat anymore.