Abstract
Every six-dimensional mathcal{N} = (2, 0) SCFT on R6 contains a set of protected operators whose correlation functions are controlled by a two-dimensional chiral algebra. We provide an alternative construction of this chiral algebra by performing an Ω-deformation of a topological-holomorphic twist of the mathcal{N} = (2, 0) theory on R6 and restricting to the cohomology of a specific supercharge. In addition, we show that the central charge of the chiral algebra can be obtained by performing equivariant integration of the anomaly polynomial of the six-dimensional theory. Furthermore, we generalize this construction to include orbifolds of the R4 transverse to the chiral algebra plane.
Highlights
We studied an alternative derivation of the chiral algebra associated with a 6d
Which is relevant for the chiral algebras associated with 4d N = 2 SCFTs
2 this operation does not deform the theory and the cohomology of the QΩ supercharge leads to the same chiral algebra on R2 as in [7]
Summary
We have presented a procedure which involves topological twists and an Ω-. deformation of the 6d N = (2, 0) SCFT and leads to a set of invariant supercharges which are identical to the ones used in [7] to arrive at a chiral algebra on C. Recall that the general 6d N = (2, 0) SCFT, labeled by a choice of a laced Lie algebra g = {AN , DN , E6,7,8}, is intrinsically strongly coupled and lacks a (known) Lagrangian formulation that manifests all its symmetries This prohibits a direct derivation by path integral methods of the conjecture in [7] that the chiral algebra associated to this 6d N = (2, 0) SCFT is the Wg algebra. While it will be nice to derive this result more rigorously, we will take it at face value and proceed to bosonize this chiral fermion and find a u(1) Kac-Moody algebra on C This is in harmony with the result in [7] for the chiral algebra arising from the N = (2, 0) free tensor multiplet. We hope that the procedure outlined above will shed more light on this connection
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