Momentum modes of M5-branes in a 2d space

TL;DR

This paper explores the structure and interactions of selfdual strings on M5-branes, revealing new modes and couplings that extend beyond standard matrix interactions, with implications for 6d field theories.

Contribution

It introduces a detailed analysis of momentum modes of M5-branes via selfdual strings, highlighting novel interactions and the role of 3-string junctions in non-standard couplings.

Findings

Selfdual strings form a 6d field with specific degrees of freedom.

Interactions depend on string orientation, deviating from standard matrix multiplication.

3-string junctions may mediate complex couplings.

Abstract

We study M5 branes by considering the selfdual strings parallel to a plane. With the internal oscillation frozen, each selfdual string gives a 5d SYM field. All selfdual strings together give a 6d field with 5 scalars, 3 gauge degrees of freedom and 8 fermionic degrees of freedom in adjoint representation of U(N). Selfdual strings with the same orientation have the SYM-type interaction. For selfdual strings with the different orientations, which could also be taken as the unparallel momentum modes of the 6d field on that plane or the (p,q) (r,s) strings on D3 with (p,q)\neq (r,s), the [i,j]+[j,k]\rightarrow [i,k] relation is not valid, so the coupling cannot be written in terms of the standard N \times N matrix multiplication. 3-string junction, which is the bound state of the unparallel [i,j] [j,k] selfdual strings, may play a role here.