BPS index and 4d N=2 superconformal field theories

TL;DR

This paper analyzes the BPS index in 4d N=2 superconformal field theories, revealing its structure through compactifications of E-string theory and determining key invariants and exponents.

Contribution

It provides a detailed characterization of the BPS index for specific 4d N=2 SCFTs using compactification techniques, identifying fundamental invariants and exponents.

Findings

Characterized the BPS index by two exponents and a sequence of invariants.

Determined the exponents and first few invariants of the BPS index.

Clarified the structure of the BPS index in these theories.

Abstract

We study the BPS index for the four-dimensional rank-one N=2 superconformal field theories H_0, H_1, H_2, E_6, E_7, E_8. We consider compactifications of the E-string theory on T^2 in which these theories arise as low energy limits. Using this realization we clarify the general structure of the BPS index. The index is characterized by two exponents and a sequence of invariants. We determine the exponents and the first few invariants.