Null M5 brane symmetries.

在我的研究中，我研究了(2，0)理论的零约化，得到了重合零M5膜的世界体积理论。这些理论特别令人感兴趣，因为尽管它们打破了六维洛伦兹对称，但我们能够写下重现运动方程的作用，并且在超对称的四分之三以下是不变的。准确地说，我们证明了超共形对称群通过这种从OSP(8*|4)到OSP(6|4)的非标准实现而被打破。值得注意的是，这与在ABJM的原始公式中观察到的对称性破缺完全相同，只是在OSP(8*|4)的偶数部分，R对称性和时空对称性的滚动是颠倒的。更值得注意的是，人们可以在这两种情况下使用u(1)算符来完成理论的谱到它们的未破缺形式，在ABJM中，这是由6D理论中的单极算符通过瞬子算符来实现的。这些相似之处提出了一个问题，我们能否寻找6D理论的破缺对称代数的杨氏扩张，实际上，这与ABJM情况下的代数完全相同。如果对称代数可以推广到杨氏代数，唯一的区别是我们对这些零理论有作用。最近，在将杨氏代数的非局部对称性直接应用于作用量和运动方程方面，已经有了令人兴奋的工作。我的意图是将OSP(6|4)的杨安扩展应用于我们对空M5膜的操作。这一计算结果可以作为6DSCFT可积性的证据。也有(1，0)6D SCFT的情况，我们的归零法也为其提供了作用，故事是不同的，因为原始的超共形代数不同于ABJM，但不是OSP(8*|2)。但这仍然是一个非常相关的问题，可能对于某些数量的超多重态和色，我们也可以观察到杨氏对称性。

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.