Genus two modular bootstrap
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We study the Virasoro conformal block decomposition of the genus two partition function of a two-dimensional CFT by expanding around a ℤ3-invariant Riemann surface that is a three-fold cover of the Riemann sphere branched at four points, and explore constraints from genus two modular invariance and unitarity. In particular, we find “critical surfaces” that constrain the structure constants of a CFT beyond what is accessible via the crossing equation on the sphere.
KeywordsConformal and W Symmetry Conformal Field Theory
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- A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].
- D. Friedan and S.H. Shenker, The Analytic Geometry of Two-Dimensional Conformal Field Theory, Nucl. Phys. B 281 (1987) 509 [INSPIRE].
- A. Maloney, Notes on the renyi surface, private communication.Google Scholar
- D. Simmons-Duffin, The Conformal Bootstrap, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (TASI 2015), Boulder, CO, U.S.A., June 1-26, 2015, pp. 1-74 (2017) [DOI: https://doi.org/10.1142/9789813149441_0001] [arXiv:1602.07982] [INSPIRE].