The (2, 0) superalgebra, null M-branes and Hitchin’s system

Abstract

We present an interacting system of equations with sixteen supersymmetries and an SO(2) × SO(6) R-symmetry where the fields depend on two space and one null dimensions that is derived from a representation of the six-dimensional (2, 0) superalgebra. The system can be viewed as two M5-branes compactified on S 1 − ×T 2 or equivalently as M2-branes on R + × R 2 , where ± refer to null directions. We show that for a particular choice of fields the dynamics can be reduced to motion on the moduli space of solutions to the Hitchin system. We argue that this provides a description of intersecting null M2-branes and is also related by U-duality to a DLCQ description of four-dimensional maximally supersymmetric Yang-Mills.

Supersymmetric soliton σ-models from non-Lorentzian field theories

“…One would expect these symmetries to descend to the quantum mechanical model. Finally, it would be of interest to revisit the non-Lorentzian theories descended from the (1+2)dimensional BLG and ABJM/ABJ Chern-Simons-matter theories, which describe a configuration of M2-branes that is U-dual to the lightcone M5-brane configuration discussed in this paper [16,31]. The reduced theory would then be a σ-model on Hitchin moduli space [32], again extended to include couplings to additional fields in the parent theory.…”

Non-Lorentzian RG flows and supersymmetry

“…We now turn our attention to similar limits of worldvolume theories for multiple M2-branes. In [23], a non-Lorentzian variant of the N = 8 BLG theory was constructed from the (2, 0) system of [25,26]. It was further explained that this system is U-dual to the DLCQ description of M5-branes.…”

“…However, in this more general construction, we see that all 32 supersymmetries of the original N = 8 theory survive in the limiting theory. As discussed in [23] the dynamics is restricted to a three-algebra variation of the Hitchin system for SU (2) gauge group.…”

M‐Branes: Lessons from M2's and Hopes for M5's

“…We can also take a null which leads to a rather odd system. In particular the fields depend only on and now are non‐zero.…”

“…Phys. 2019, 67,1910011 i.e. 5D MSYM, corresponding to M5-brane on S 1 and KK-modes are instanton-solitons:…”