Torons and D-Brane Bound States

TL;DR

This paper explores the interpretation of instantons on a torus with twisted boundary conditions as bound states of branes, revealing how SU(N) and U(1) components contribute to instanton numbers and analyzing the geometric properties of these solutions.

Contribution

It introduces a novel interpretation of instantons as brane bound states and examines the fractional contributions of SU(N) and U(1) parts to the instanton number.

Findings

Bound states of branes can be constructed from twisted instantons.

SU(N) and U(1) parts contribute fractional instanton numbers.

Geometry of two-cycles in $T^4$ informs properties of solutions.

Abstract

We interpret instantons on a torus with twisted boundary conditions, in terms of bound states of branes. The interplay between the SU(N) and U(1) parts of the U(N) theory of N 4-branes allows the construction of a variety of bound states. The SU(N) and U(1) parts can contribute fractional amounts to the total instanton number which is integral. The geometry of non-self intersecting two-cycles in $T^4$ sheds some light on a number of properties of these solutions.