BPS Spectrum, Indices and Wall Crossing in N=4 Supersymmetric Yang-Mills Theories

TL;DR

This paper introduces protected indices for BPS states in N=4 supersymmetric SU(N) gauge theories, providing a wall crossing formula to compute the spectrum across the moduli space, enhancing understanding of quantum states in these theories.

Contribution

It presents new protected indices for BPS states, derives their wall crossing formula, and demonstrates how to compute these indices throughout the moduli space.

Findings

Protected indices effectively capture BPS spectrum information.

Wall crossing formula enables spectrum computation at all moduli points.

Representation of BPS states as planar string networks on D3-branes.

Abstract

BPS states in N=4 supersymmetric SU(N) gauge theories in four dimensions can be represented as planar string networks with ends lying on D3-branes. We introduce several protected indices which capture information on the spectrum and various quantum numbers of these states, give their wall crossing formula and describe how using the wall crossing formula we can compute all the indices at all points in the moduli space.