Comments on s-rule violating configurations in field theory

TL;DR

This paper constructs specific boundary configurations in N=4 supersymmetric Yang-Mills theory, demonstrating s-rule violations for N>1 and analyzing their energy relative to BPS bounds.

Contribution

It explicitly constructs and analyzes boundary configurations in N=4 SYM that violate the s-rule, providing energy calculations for these non-supersymmetric states.

Findings

Configurations violate the s-rule for N>1

Energy is proportional to N(N^2-1) g_{YM4}^{-2} L^{-3}

Configurations are non-supersymmetric

Abstract

We explicitly construct a configuration of ${\cal N}=4$ supersymmetry Yang-Mills theory with gauge group $U(N)$ on an interval on length $L$ with a D5-like boundary condition on one end and an NS5-like boundary condition on the other. For $N>1$, such a configuration violates the $s$-rule and is non-supersymmetric. We compute the energy relative to the BPS bound of these configurations and find that it is proportional to $N(N^2-1) g_{YM4}^{-2} L^{-3}$.