Advances in Theoretical and Mathematical Physics

Volume 22 (2018)

Number 6

Bootstrapping chiral CFTs at genus two

Pages: 1447 – 1487

DOI: http://dx.doi.org/10.4310/ATMP.2018.v22.n6.a3

Authors

Christoph A. Keller (Department of Mathematics, Eidgenössische Technische Hochschule (ETH), Zürich, Switzerland)

Grégoire Mathys (Department of Physics, Eidgenössische Technische Hochschule (ETH), Zürich, Switzerland)

Ida G. Zadeh (Department of Mathematics, Eidgenössische Technische Hochschule (ETH), Zürich, Switzerland)

Abstract

Genus two partition functions of 2d chiral conformal field theories are given by Siegel modular forms. We compute their conformal blocks and use them to perform the conformal bootstrap. The advantage of this approach is that it imposes crossing symmetry of an infinite family of four point functions and also modular invariance at the same time. Since for a fixed central charge the ring of Siegel modular forms is finite dimensional, we can perform this analytically. In this way we derive bounds on three point functions and on the spectrum of such theories.

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Published 3 May 2019