A note on E-strings

TL;DR

This paper investigates BPS states in type IIA string theory on a local Calabi-Yau 3-fold, relating them to E-string states, and uses mirror symmetry transformations to compute their generating functions.

Contribution

It introduces a method using Picard-Lefshetz transformations to relate D-brane configurations and derive BPS state generating functions.

Findings

Derived automorphisms of K-theory for the Calabi-Yau divisor.

Mapped D-brane configurations to bound states involving D4 and D0-branes.

Provided explicit generating functions for BPS state multiplicities.

Abstract

We study BPS states in type IIA string compactification on a local Calabi-Yau 3-fold which are related to the BPS states of the E-string. Using Picard-Lefshetz transformations of the 3-cycles on the mirror manifold we determine automorphisms of the K-theory of the compact divisor of the Calabi-Yau which maps certain D-brane configurations to a bound state of single D4-brane with multiple D0-branes. This map allows us to write down the generating functions for the multiplicity of these BPS states.