Unraveling the holomorphic twist: central charges

Internet publication

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 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.

Authors: Bomans, P; Wu, J

• Publication status: Published
• Peer review status: Not peer reviewed
• Publication date: 2023-11-07
• DOI: 10.48550/arXiv.2311.04304
• Language: English
• Keywords: math.MP; math-ph; hep-th