Matrix String Theory, 2D SYM Instantons and affine Toda systems

TL;DR

This paper demonstrates the existence of classical BPS instantons in U(N) SYM Matrix theory that facilitate string joining and splitting, constructed via branched Riemann surface coverings and affine Toda field theories.

Contribution

It extends previous work by explicitly constructing instantons in Matrix theory using affine Toda systems, linking gauge theory and string interactions.

Findings

Existence of BPS instantons in U(N) SYM Matrix theory.

Explicit construction using branched Riemann surfaces.

Connection to affine Toda field theories.

Abstract

Extending a recent result of S.B. Giddings, F. Hacquebord and H. Verlinde, we show that in the U(N) SYM Matrix theory there exist classical BPS instantons which interpolate between different closed string configurations via joining/splitting interactions similar to those of string field theory. We construct them starting from branched coverings of Riemann surfaces. For the class of them which we analyze in detail the construction can be made explicit in terms U(N) affine Toda field theories.