Twists of superconformal algebras

Fuente: arXiv
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Main Authors: Elliott, Chris, Gwilliam, Owen, Lotito, Matteo
Format: Preprint
Published: 2024
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author Elliott, Chris
Gwilliam, Owen
Lotito, Matteo
author_facet Elliott, Chris
Gwilliam, Owen
Lotito, Matteo
contents We take first steps toward a theory of ``conformal twists'' for superconformal field theories in dimension 3 to 6, extending the well-known analysis of twists for supersymmetric theories. A conformal twist is a square-zero odd element in the superconformal Lie algebra, and we classify all twists and describe their orbits under the adjoint action of the superconformal group. 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. Conformal twists can give rise to interesting subalgebras and protected sectors of operators in a superconformal field theory, with the Donaldson--Witten topological field theory and the vertex operator algebras of 4-dimensional N=2 SCFTs being prominent examples. To obtain mathematical precision, we explain how to extract vertex algebras and E_n algebras from a twisted superconformal field theory using factorization algebras.
format Preprint
id arxiv_https___arxiv_org_abs_2403_19753
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Twists of superconformal algebras
Elliott, Chris
Gwilliam, Owen
Lotito, Matteo
Mathematical Physics
High Energy Physics - Theory
Representation Theory
We take first steps toward a theory of ``conformal twists'' for superconformal field theories in dimension 3 to 6, extending the well-known analysis of twists for supersymmetric theories. A conformal twist is a square-zero odd element in the superconformal Lie algebra, and we classify all twists and describe their orbits under the adjoint action of the superconformal group. 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. Conformal twists can give rise to interesting subalgebras and protected sectors of operators in a superconformal field theory, with the Donaldson--Witten topological field theory and the vertex operator algebras of 4-dimensional N=2 SCFTs being prominent examples. To obtain mathematical precision, we explain how to extract vertex algebras and E_n algebras from a twisted superconformal field theory using factorization algebras.
title Twists of superconformal algebras
topic Mathematical Physics
High Energy Physics - Theory
Representation Theory
url https://arxiv.org/abs/2403.19753