On instantons as Kaluza-Klein modes of M5-branes

TL;DR

This paper investigates the relationship between instantons, W-bosons, and Kaluza-Klein modes in 5d maximally supersymmetric Yang-Mills theory derived from 6d (2,0) theory, revealing new insights into BPS states and worldsheet degrees.

Contribution

It demonstrates the existence of unique bound states of noncommutative U(1) instantons and links charged instantons to self-dual string degeneracies, introducing novel momentum-carrying degrees on the worldsheet.

Findings

Existence of unique threshold bound states for U(1) instantons.

Charged instantons match SU(2) self-dual string degeneracies.

Discovery of momentum-carrying degrees on the worldsheet related to anomaly coefficients.

Abstract

Instantons and W-bosons in 5d maximally supersymmetric Yang-Mills theory arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding self-dual strings, respectively. We study an index which counts BPS instantons with electric charges in Coulomb and symmetric phases. We first prove the existence of unique threshold bound state of (noncommutative) U(1) instantons for any instanton number, and also show that charged instantons in the Coulomb phase correctly give the degeneracy of SU(2) self-dual strings. By studying SU(N) self-dual strings in the Coulomb phase, we find novel momentum-carrying degrees on the worldsheet. The total number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory. We finally show that our index can be used to study the symmetric phase of this theory, and provide an interpretation as the superconformal index of the sigma model on instanton moduli space.