Vector Bundle Moduli and Small Instanton Transitions

TL;DR

This paper provides a comprehensive method for calculating moduli of stable SU(n) vector bundles on elliptically fibered Calabi-Yau threefolds, with explicit results for Hirzebruch bases, and explores the origin and enumeration of transition moduli from small instanton phase transitions.

Contribution

It introduces a general prescription for computing vector bundle moduli and details the enumeration of transition moduli arising from small instanton transitions, including explicit examples and alternative descriptions.

Findings

Explicit formulas for vector bundle moduli on Hirzebruch bases

Enumeration of transition moduli from small instanton phase transitions

Alternative description of transition moduli as sections of vector bundles

Abstract

We give the general presciption for calculating the moduli of irreducible, stable SU(n) holomorphic vector bundles with positive spectral covers over elliptically fibered Calabi-Yau threefolds. Explicit results are presented for Hirzebruch base surfaces B=F_r. The transition moduli that are produced by chirality changing small instanton phase transitions are defined and specifically enumerated. The origin of these moduli, as the deformations of the spectral cover restricted to the ``lift'' of the horizontal curve of the M5-brane, is discussed. We present an alternative description of the transition moduli as the sections of rank n holomorphic vector bundles over the M5-brane curve and give explicit examples. Vector bundle moduli appear as gauge singlet scalar fields in the effective low-energy actions of heterotic superstrings and heterotic M-theory.