Unravelling the Holomorphic Twist: Central Charges
Year: 2024
Type: article
Abstract: 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 $$\mathcal {N}=1$$ 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 $$\lambda $$ 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.
Authors: Pieter Bomans, Jingxiang Wu
Institution: University of Oxford
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
Awards: G5169949119, G539914721, G7955930135
OpenAlex ID: W4404400079