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Genus two partition functions of chiral conformal field theories

Gaberdiel, Matthias R. and Keller, Christoph A. and Volpato, Roberto (2010) Genus two partition functions of chiral conformal field theories. Communications in Number Theory and Physics, 4 (2). pp. 295-363. ISSN 1931-4523. doi:10.4310/CNTP.2010.v4.n2.a2.

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A systematic analysis of the genus two vacuum amplitudes of chiral self-dual conformal field theories is performed. It is explained that the existence of a modular invariant genus two partition function implies infinitely many relations among the structure constants of the theory. All of these relations are shown to be a consequence of the associativity of the operator product expansion, as well as the modular covariance properties of the torus one-point functions. U sing these techniques we prove that for the proposed extremal conformal field theories at c = 24k a consistent genus two vacuum amplitude exists for all k, but that this does not actually check the consistency of these theories beyond what is already testable at genus one.

Item Type:Article
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Keller, Christoph A.0000-0003-2592-2012
Additional Information:© 2010 International Press. Received March 4, 2010. We thank Terry Gannon for a useful conversation and subsequent correspondence. C.A.K. thanks the Pauli Center for support during his visit to ETH. The research of M.R.G. is partially supported by the Swiss National Science Foundation, while the research of R.V. is supported by an INFN Fellowship.
Group:Caltech Theory
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)UNSPECIFIED
Istituto Nazionale di Fisica Nucleare (INFN)UNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20101118-114657861
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20893
Deposited On:19 Nov 2010 23:10
Last Modified:09 Nov 2021 00:04

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