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arXiv · 2310.15563

Twisted Verlinde formula for vertex operator algebras

Chongying Dong·Xingjun Lin
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Abstract

For a rational and $C_2$-cofinite vertex operator algebra $V$ with an automorphism group $G$ of prime order, the fusion rules for twisted $V$-modules are studied, a twisted Verlinde formula which relates fusion rules for $g$-twisted modules to the $S$-matrix in the orbifold theory is established. As an application of the twisted Verlinde formula, a twisted analogue of the Kac-Walton formula is proved, which gives fusion rules between twisted modules of affine vertex operator algebras in terms of Clebsch-Gordan coefficients associated to the corresponding finite dimensional simple Lie algebras.

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Chongying Dong, Xingjun Lin. 2023-10-24. Twisted Verlinde formula for vertex operator algebras. https://arxiv.org/abs/2310.15563

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