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Twists of superconformal algebras
Published 28 Mar 2024 in math-ph, hep-th, math.MP, and math.RT | (2403.19753v2)
Abstract: We develop the theory of "conformal twists" of superconformal field theories in dimensions 3 to 6, extending the well-known analysis of twists for supersymmetric theories. The conformal twists describe all possible inequivalent choices of a nilpotent element in the superconformal algebra. Such twists can give rise to interesting subalgebras and protected sectors of operators, with the Donaldson--Witten topological field theory and the vertex operator algebras of 4-dimensional N=2 SCFTs being prominent examples. We work mostly with the complexified superconformal algebras, unless explicitly stated otherwise; real forms of the superconformal algebra may have important physical implications, but we only discuss these subtleties in a few special cases. To obtain mathematical precision, we explain how to extract vertex algebras and E_n algebras from a twisted superconformal field theory using factorization algebras.
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