Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 295-364 |
| Number of pages | 70 |
| Journal | Communications in Number Theory and Physics |
| Volume | 4 |
| Issue number | 2 |
| State | Published - Jun 1 2010 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Algebra and Number Theory
- Mathematical Physics
- Physics and Astronomy(all)
Cite this
Genus two partition functions of chiral conformal field theories. / Gaberdiel, Matthias R.; Keller, Christoph A.; Volpato, Roberto.
In: Communications in Number Theory and Physics, Vol. 4, No. 2, 01.06.2010, p. 295-364.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Genus two partition functions of chiral conformal field theories
AU - Gaberdiel, Matthias R.
AU - Keller, Christoph A.
AU - Volpato, Roberto
PY - 2010/6/1
Y1 - 2010/6/1
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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UR - http://www.scopus.com/inward/citedby.url?scp=80053099177&partnerID=8YFLogxK
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 -