Small Instantons in String Theory

TL;DR

This paper investigates the behavior of small instantons in heterotic string theory, revealing that zero-size instantons lead to enhanced gauge symmetries, providing insights into non-perturbative phenomena and string duality puzzles.

Contribution

It demonstrates that zero-size instantons induce extra gauge symmetries in heterotic strings, connecting non-perturbative effects to gauge symmetry enhancement and duality.

Findings

Enhanced gauge symmetry Sp(k) when k instantons collapse

Quantum vacua with higher gauge rank than conformal field theory

Non-perturbative phenomena cannot be suppressed by weak coupling

Abstract

A long-standing puzzle about the heterotic string has been what happens when an instanton shrinks to zero size. It is argued here that the answer at the quantum level is that an extra $SU(2)$ gauge symmetry appears that is supported in the core of the instanton. Thus in particular the quantum heterotic string has vacua with higher rank than is possible in conformal field theory. When $k$ instantons collapse at the same point, the enhanced gauge symmetry is $Sp(k)$. These results, which can be tested by comparison to Dirichlet five-branes of Type I superstrings and to the ADHM construction of instantons, give the first example for the heterotic string of a non-perturbative phenomenon that cannot be turned off by making the coupling smaller. They have applications to several interesting puzzles about string duality.