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arXiv · 2407.08220

Conformal field theory of Gaussian free fields in a multiply connected domain

Tom Alberts·Sung-Soo Byun·Nam-Gyu Kang
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Abstract

We implement a version of conformal field theory (CFT) that gives a connection to SLE in a multiply connected domain. Our approach is based on the Gaussian free field and applies to CFTs with central charge $c \leq 1$. In this framework we introduce the generalized Eguchi-Ooguri equations and use them to derive the explicit form of Ward's equations, which describe the insertion of a stress tensor in terms of Lie derivatives and differential operators depending on the Teicm\"{u}ller modular parameters. Furthermore, by implementing the BPZ equations, we provide a conformal field theoretic realization of an SLE in a multiply connected domain, which in particular suggests its drift function, and construct a class of martingale observables for this SLE process.

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Tom Alberts, Sung-Soo Byun, Nam-Gyu Kang. 2024-07-11. Conformal field theory of Gaussian free fields in a multiply connected domain. https://arxiv.org/abs/2407.08220

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