M2-branes and the (2, 0) superalgebra

Abstract

We present a generalization of the six-dimensional (2, 0) system of arXiv:1007.2982 to include a constant abelian 3-form. For vanishing 3-form this system is known to provide a variety descriptions of parallel M5-branes. For a particular choice of 3-form the system is shown to reduce to that of two M2-branes. Thus this generalised (2, 0) system provides a unified description of two parallel M2-branes or M5-branes.

Non-Lorentzian field theories with maximal supersymmetry and moduli space dynamics

“…The on-shell conditions now reduce to motion on the moduli space of solutions to the Hitchin System, this time for any gauge group. However although it has the same number of supersymmetries as the M2-brane case discussed above it only has SO(2) × SO(5) R-symmetry, not SO(2) × SO (6). It is natural to postulate that, just as the lorentzian M2-brane theory is the strong coupling limit of (2+1)-dimensional maximally supersymmetric Yang-Mills (which can be viewed as the dimensional reduction of the M5-brane), the null M2-brane theory (2.5) is the strong coupling fixed point of the null M5-brane action (3.20) in the case of an SU(2) gauge group.…”

“…where now the i index has been reduced to i = 1, .., d with a = d + 1, .., 4 and as before we have I = 6,7,8,9,10. Note also that anti-self-duality implies that the various components (G ij , G ia , G ab ) are not independent.…”

“…so that the fields have canonical scaling dimensions. 3 The hat arises as this basis is adapted from M5-branes to M2-branes in the construction of [6,7] but this distinction is not necessary here and can be dropped. sixteen supersymmetries derived in [7]:…”

“…In [5,6] a non-abelian system of equations was formulated which provide a representation of the six-dimensional (2, 0) superalgebra. The system involves a set of dynamical equations as well as some constraint equations.…”

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

“…Finally in this last section I wanted to indulge myself by reporting on my own recent work that I hope is of interest to the conference crowd and I welcome any suggestions. In particular in [60,61] my collaborators and I constructed a representation of the (2,0) superalgebra acting on a set of fields:…”