BPS spectroscopy with reinforcement learning

TL;DR

This paper introduces a reinforcement learning approach to efficiently determine the finiteness and full spectrum of BPS states in 4d N=2 quantum field theories, outperforming brute-force methods.

Contribution

It presents a novel RL-based algorithm for identifying BPS spectra and minimal chambers in N=2 QFTs, enabling solutions previously computationally infeasible.

Findings

RL model converges faster than brute-force scans

Successfully identifies all minimal chambers of SU(2) Nf=4 theory

Discovers new minimal chambers in geometrically engineered theories

Abstract

We apply reinforcement learning (RL) to establish whether at a given position in the Coulomb branch of the moduli space of a 4d $\mathcal{N} = 2$ quantum field theory (QFT) the BPS spectrum is finite. If it is, we furthermore determine the full BPS spectrum at such point in moduli space. We demonstrate that using a RL model one can efficiently determine the suitable sequence of quiver mutations of the BPS quiver that will generate the full BPS spectrum. We analyse the performance of the RL model on random BPS quivers and show that it converges to a solution various orders of magnitude faster than a systematic brute-force scan. As a result, we show that our algorithm can be used to identify all minimal chambers of a given $\mathcal{N}=2$ QFT, a task previously intractable with computer scanning. As an example, we recover all minimal chambers of the $\text{SU}(2)$ $N_f = 4$ gauge theory, and discover new minimal chambers for theories that can be realized by IIB geometric engineering.