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Main Authors: Bomans, Pieter, Wu, Jingxiang
Format: Preprint
Published: 2023
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Online Access:https://arxiv.org/abs/2311.04304
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author Bomans, Pieter
Wu, Jingxiang
author_facet Bomans, Pieter
Wu, Jingxiang
contents The holomorphic twist provides a powerful framework to study minimally protected sectors in supersymmetric quantum field theories. We investigate the algebraic structure underlying the holomorphic twist of $\mathcal{N} = 1$ superconformal field theories in four dimensions. In particular, in holomorphically twisted theories the flavour and conformal symmetry algebras are enhanced to infinite-dimensional higher Kac Moody and higher Virasoro symmetry algebras respectively. We explicitly compute the binary and ternary $λ$-brackets and clarify their relation with the underlying infinite-dimensional symmetry algebra. Doing so we show that the central extensions of said symmetry algebras precisely encode the conformal anomalies $a$ and $c$ as well as the flavour central charges of the physical four-dimensional theory. This parallels the familiar story in two dimensions where the conformal anomaly $c$ is encoded in the central extension of the Virasoro algebra.
format Preprint
id arxiv_https___arxiv_org_abs_2311_04304
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Unravelling the Holomorphic Twist: Central Charges
Bomans, Pieter
Wu, Jingxiang
High Energy Physics - Theory
Mathematical Physics
The holomorphic twist provides a powerful framework to study minimally protected sectors in supersymmetric quantum field theories. We investigate the algebraic structure underlying the holomorphic twist of $\mathcal{N} = 1$ superconformal field theories in four dimensions. In particular, in holomorphically twisted theories the flavour and conformal symmetry algebras are enhanced to infinite-dimensional higher Kac Moody and higher Virasoro symmetry algebras respectively. We explicitly compute the binary and ternary $λ$-brackets and clarify their relation with the underlying infinite-dimensional symmetry algebra. Doing so we show that the central extensions of said symmetry algebras precisely encode the conformal anomalies $a$ and $c$ as well as the flavour central charges of the physical four-dimensional theory. This parallels the familiar story in two dimensions where the conformal anomaly $c$ is encoded in the central extension of the Virasoro algebra.
title Unravelling the Holomorphic Twist: Central Charges
topic High Energy Physics - Theory
Mathematical Physics
url https://arxiv.org/abs/2311.04304