### Instanton - a window into physics of M5-branes

## Abstract

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 U(1) instantons for

any instanton number. 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 propose 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.