Comments on chiral algebras and $\Omega$-deformations

Abstract

Every six-dimensional $\mathcal{N}=(2,0)$ SCFT on ${\mathbf{R}}^6$ 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 $\Omega$-deformation~of a topological-holomorphic twist of the $\mathcal{N}=(2,0)$ theory on ${\mathbf{R}}^6$ 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 ${\mathbf{R}}^4$ transverse to the chiral algebra plane.

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Cited by in corpus (5)

• Five-Dimensional Non-Lorentzian Conformal Field Theories and their Relation to Six-Dimensions
• $d>2$ Stress-Tensor OPE near a Line
• Twisted holography of defect fusions
• Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories