Extremal Transitions in Heterotic String Theory

TL;DR

This paper investigates extremal transitions in heterotic string compactifications, focusing on changes in Calabi-Yau manifolds and gauge bundles, and explores the description of small instantons within this framework.

Contribution

It introduces a unified approach to describe extremal bundle transitions and small instantons in heterotic string theory using recent mathematical language.

Findings

Bundle transitions are effectively described using Friedman, Morgan, Witten's framework.

Small instantons are characterized by specific sheaves in the same language.

The methods provide consistency checks for describing heterotic string transitions.

Abstract

In this paper we study extremal transitions between heterotic string compactifications, i.e., transitions between pairs (M,V) where M is a Calabi-Yau manifold and V a gauge bundle. Bundle transitions are described using language recently espoused by Friedman, Morgan, Witten. In addition, partly as a check on our methods, we also study how small instantons are described in the same language, and also describe the sheaves corresponding to small instantons.