Momentum Modes of M5-branes in a 2d Space

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) 6 = (r, s), the [i, j] + [j, k] → [i, k] relation is not valid, so the coupling cannot be written in terms of the standard N ×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