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 -