M-Strings

TL;DR

This paper computes the elliptic genus of M-strings, revealing their relation to supersymmetric sigma models and dual gauge theories, and explores domain wall configurations in M-theory.

Contribution

It provides the first detailed computation of the elliptic genus of M-strings, connecting it to (4,4) and (4,0) sigma models and dual 6d gauge theories.

Findings

Elliptic genus of N M-strings matches (4,0) sigma models on symmetric products for N>1.

For N=1, the elliptic genus coincides with the (4,4) case.

Computed elliptic genus of domain walls separating different M2 brane configurations.

Abstract

M2 branes suspended between adjacent parallel M5 branes lead to light strings, the `M-strings'. In this paper we compute the elliptic genus of M-strings, twisted by maximally allowed symmetries that preserve 2d (2,0) supersymmetry. In a codimension one subspace of parameters this reduces to the elliptic genus of the (4,4) supersymmetric A_{n-1} quiver theory in 2d. We contrast the elliptic genus of N M-strings with the (4,4) sigma model on the N-fold symmetric product of R^4. For N=1 they are the same, but for N>1 they are close, but not identical. Instead the elliptic genus of (4,4) N M-strings is the same as the elliptic genus of (4,0) sigma models on the N-fold symmetric product of R^4, but where the right-moving fermions couple to a modification of the tangent bundle. This construction arises from a dual A_{n-1} quiver 6d gauge theory with U(1) gauge groups. Moreover we compute the elliptic genus of domain walls which separate different numbers of M2 branes on the two sides of the wall.