Self-dual Strings and 2D SYM

TL;DR

This work analyzes M2-branes suspended between M5-branes using the ABJM model with half-BPS boundaries, showing that for small M5 separation the worldvolume theory reduces to a 2D $N=(4,4)$ super Yang–Mills-like theory whose gauge coupling depends on brane positions. It contrasts this ABJM slab with a dual IIA brane construction, studies the elliptic genus of both descriptions, and employs localization and Jeffrey–Kirwan residues to extract a Young-diagram sum for the SU($N$) sector under certain conditions. The results reveal only partial agreement between the ABJM slab and IIA descriptions, highlighting subtleties in boundary dynamics, KK modes, and global symmetry enhancements, and illustrating the need for careful accounting of boundary degrees of freedom and additional contributions to achieve an exact match. The work advances understanding of self-dual strings in M-theory, clarifying how 2D gauge dynamics emerge from higher-dimensional brane systems and clarifying the role of $q$-deformed YM structures and Higgs-branch localization in this context.

Abstract

We study the system of M2-branes suspended between parallel M5-branes using ABJM model with a natural half-BPS boundary condition. For small separation between M5-branes, the worldvolume theory is shown to reduce to a 2D N=(4,4) super Yang-Mills theory with some similarity to q-deformed Yang-Mills theory. The gauge coupling is related to the position of the branes in an interesting manner. The theory is considerably different from the 2D theory proposed for multiple "M-strings". We make a detailed comparison of elliptic genus of the two descriptions and find only a partial agreement.