Investigating the BPS Spectrum of Non-Critical E_n Strings

TL;DR

This paper analyzes the BPS spectrum of non-critical $E_n$ strings using effective actions, revealing detailed $E_n$ structures and universal degeneracy features through mirror symmetry and character expansions.

Contribution

It introduces a method to compute the BPS spectrum of $E_n$ non-critical strings via asymptotic expansions and mirror maps, providing new insights into their $E_n$ structure.

Findings

Derived the $E_n$ character expansion of the BPS spectrum.

Connected the spectrum computation to mirror symmetry on Calabi-Yau manifolds.

Identified universal degeneracy patterns independent of $E_n$.

Abstract

We use the effective action of the $E_n$ non-critical strings to study its BPS spectrum for $0 \le n \le 8$. We show how to introduce mass parameters, or Wilson lines, into the effective action, and then perform the appropriate asymptotic expansions that yield the BPS spectrum. The result is the $E_n$ character expansion of the spectrum, and is equivalent to performing the mirror map on a Calabi-Yau with up to nine K\"ahler moduli. This enables a much more detailed examination of the $E_n$ structure of the theory, and provides extensive checks on the effective action description of the non-critical string. We extract some universal ($E_n$ independent) information concerning the degeneracies of BPS excitations.