Wild Wall Crossing and BPS Giants

TL;DR

This paper reveals that in pure SU(3) N=2 super Yang-Mills theory, the BPS spectrum can grow exponentially in certain regions, with spectral networks and wall-crossing methods used to analyze this phenomenon.

Contribution

It demonstrates the existence of exponential BPS spectrum growth in SU(3) N=2 super Yang-Mills and illustrates the use of spectral networks and wall-crossing formulas in this context.

Findings

Exponential growth of BPS degeneracies in certain Coulomb branch regions.

Spectral networks effectively determine the four-dimensional BPS spectrum.

Identification of unexplained regularities in the BPS spectrum.

Abstract

We show that the BPS spectrum of pure SU(3) four-dimensional super Yang-Mills with N=2 supersymmetry exhibits a surprising phenomenon: there are regions of the Coulomb branch where the growth of the BPS degeneracies with the charge is exponential. We show this using spectral networks and independently using wall-crossing formulae and quiver methods. The computations using spectral networks provide a very nontrivial example of how these networks determine the four-dimensional BPS spectrum. We comment on some physical implications of the wild spectrum: for example, exponentially many field-theoretic BPS states with large charge are gigantic. Finally, we exhibit some surprising, thus far unexplained, regularities of the BPS spectrum.