The Moduli of Reducible Vector Bundles

TL;DR

This paper presents a method to compute the dimensions of moduli spaces for reducible holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds, with applications to small instanton transitions in string theory.

Contribution

It introduces a procedure for calculating moduli space dimensions of reducible bundles, specifically for poly-stable bundles arising from small instanton transitions.

Findings

Computed moduli space dimensions for specific bundle configurations.

Analyzed the structure and physical implications of small instanton transitions.

Provided insights into the geometry of vector bundles in string compactifications.

Abstract

A procedure for computing the dimensions of the moduli spaces of reducible, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds X is presented. This procedure is applied to poly-stable rank n+m bundles of the form V + pi* M, where V is a stable vector bundle with structure group SU(n) on X and M is a stable vector bundle with structure group SU(m) on the base surface B of X. Such bundles arise from small instanton transitions involving five-branes wrapped on fibers of the elliptic fibration. The structure and physical meaning of these transitions are discussed.