Null M5 brane symmetries.

In my research I study a null reduction of (2,0) theory, giving rise the world volume theory of coincident null M5 branes. These theories are of particular interest as, although they break 6d Lorentz symmetry, we are able to write down actions that reproduce the equations of motion and are invariant under 3/4ths of the super symmetry. Precisely we showed that the superconformal symmetry group is broken by this reduction from Osp(8*|4) to a non-standard realisation of Osp(6|4). The remarkable ccoincidence is that this is the exact same symmetry breaking that was observed in the original formulation of ABJM, just that in the even part of Osp(8*|4), the rolls of R-symmetry and spacetime symmetry are reversed.

What is even more remarkable, is that one can use u(1) opperators in both cases to complete the spectrum of the theories to their non-broken forms, in ABJM this is carried out by monopole operators in the 6d theory by instanton operators.

These similarities beg the question, can we look for a Yangian extension of the broken symmetry algebra of the 6d theory, indeed this is precisely the same algebra as in the ABJM case. If the symmetry algebra can be extended to a Yangian, with the unique difference being we have actions for these null theories.

There has been exciting recent work in applying the non-local symmetries of Yangian algebras directly to actions and equations of motion. It would be my intent to take the Yangian extension of Osp(6|4) and apply it to our actions for null M5 branes. The result of this calculation may serve as evidence for the integrability of the 6d SCFT.

There are also the cases of the (1,0) 6d SCFTs, for which our null reduction also provides actions, the story is different, as the original superconformal algebra is not the same as ABJM but is not Osp(8*|2). But this is still a very relevant question, and it may be the case that for certain numbers of hypermultiplets and colours, we may also observe Yangian symmetry.