@article{f6118ca995a246eca0696a90f2b9896a,

title = "Bootstrapping chiral CFTs at genus two",

abstract = "Genus two partition functions of 2d chiral conformal field theories are given by Siegel modular forms. We compute their conformal blocks and use them to perform the conformal bootstrap. The advantage of this approach is that it imposes crossing symmetry of an infinite family of four point functions and also modular invariance at the same time. Since for a fixed central charge the ring of Siegel modular forms is finite dimensional, we can perform this analytically. In this way we derive bounds on three point functions and on the spectrum of such theories.",

author = "Keller, {Christoph A.} and Gr{\'e}goire Mathys and Zadeh, {Ida G.}",

note = "Funding Information: This work is partly based on the master thesis of one of us (GM). We would like to thank Matthias Gaberdiel and Peter Goddard for sharing a draft of their upcoming book with us, and Roberto Volpato for sharing his Mathematica notebooks with us. CAK thanks the Harvard University High Energy Theory Group for hospitality. IGZ thanks Institute of Physics at the University of Amsterdam for hospitality. We thank the Galileo Galilei Institute for Theoretical Physics (GGI) for the hospitality and INFN for partial support during the completion of this work, within the program New Developments in AdS3/CFT2 Holography. In addition, IGZ thanks INFN as well as the ACRI (Associazione di Fondazioni e di Casse di Risparmio S.p.a.) for partial support through a YITP fellowship. CAK and IGZ are supported by the Swiss National Science Foundation through the NCCR SwissMAP.",

year = "2018",

doi = "10.4310/atmp.2018.v22.n6.a3",

language = "English (US)",

volume = "22",

pages = "1447--1487",

journal = "Advances in Theoretical and Mathematical Physics",

issn = "1095-0761",

publisher = "International Press of Boston, Inc.",

number = "6",

}