Instanton Moduli in String Theory

TL;DR

This paper derives formulas for the number of moduli of SU(n) vector bundles on Calabi-Yau threefolds, with implications for string theory compactifications and instanton moduli spaces.

Contribution

It provides explicit formulas and conditions for minimal moduli of vector bundles, extending methods to broader classes of Calabi-Yau threefolds.

Findings

Derived formulas for moduli counts of vector bundles

Identified conditions for minimal moduli configurations

Defined and interpreted transition moduli in phase transitions

Abstract

Expressions for the number of moduli of arbitrary SU(n) vector bundles constructed via Fourier-Mukai transforms of spectral data over Calabi- Yau threefolds are derived and presented. This is done within the context of simply connected, elliptic Calabi-Yau threefolds with base Fr, but the methods have wider applicability. The condition for a vector bundle to possess the minimal number of moduli for fixed r and n is discussed and an explicit formula for the minimal number of moduli is presented. In addition, transition moduli for small instanton phase transitions involving non-positive spectral covers are defined, enumerated and given a geometrical interpretation.