# BPS states in the Minahan-Nemeschansky $E_7$ theory

## TL;DR

This paper employs spectral networks to compute BPS degeneracies in the Minahan-Nemeschansky $E_7$ theory, revealing patterns in BPS indices related to charge multiples and extending previous calculations in the $E_6$ theory.

## Contribution

It introduces a spectral network method to calculate BPS states in the $E_7$ theory and uncovers a recurring pattern in BPS indices across different charges.

## Key findings

- BPS degeneracies follow a specific pattern related to charge multiples.
- Extended calculations of BPS states in the $E_6$ theory for larger charges.
- Confirmed the pattern of BPS indices in the $E_7$ theory.

## Abstract

We use the method of spectral networks to calculate BPS degeneracies in the Minahan-Nemeschansky $E_7$ theory, as representations of the $E_7$ flavor symmetry. Our results provide another example of a pattern noticed earlier in the Minahan-Nemeschansky $E_6$ theory: when the electromagnetic charge is $n$ times a primitive charge, the BPS index is a positive integer multiple of $(-1)^{n+1} n$. We also calculate BPS degeneracies in the Minahan-Nemeschansky $E_6$ theory for larger charges than were previously computed.