TY - JOUR
T1 - Genus two partition functions of chiral conformal field theories
AU - Gaberdiel, Matthias R.
AU - Keller, Christoph A.
AU - Volpato, Roberto
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2010/6
Y1 - 2010/6
N2 - 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. Using 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.
AB - 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. Using 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.
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U2 - 10.4310/cntp.2010.v4.n2.a2
DO - 10.4310/cntp.2010.v4.n2.a2
M3 - Article
AN - SCOPUS:80053099177
VL - 4
SP - 295
EP - 364
JO - Communications in Number Theory and Physics
JF - Communications in Number Theory and Physics
SN - 1931-4523
IS - 2
ER -