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N = 4 superconformal bootstrap of the K3 CFT

Lin, Ying-Hsuan and Shao, Shu-Heng and Simmons-Duffin, David and Wang, Yifan and Yin, Xi (2017) N = 4 superconformal bootstrap of the K3 CFT. Journal of High Energy Physics, 2017 (5). Art. No. 126. ISSN 1029-8479.

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We study two-dimensional (4, 4) superconformal field theories of central charge c = 6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the BPS N = 4 superconformal blocks with c = 6 and bosonic Virasoro conformal blocks with c = 28, and an exact result on the moduli dependence of a certain integrated BPS 4-point function. Nontrivial bounds on the non-BPS spectrum in the K3 CFT are obtained as functions of the CFT moduli, that interpolate between the free orbifold points and singular CFT points. We observe directly from the CFT perspective the signature of a continuous spectrum above a gap at the singular moduli, and find numerically an upper bound on this gap that is saturated by the A_1 N = 4 cigar CFT. We also derive an analytic upper bound on the first nonzero eigenvalue of the scalar Laplacian on K3 in the large volume regime, that depends on the K3 moduli data. As two byproducts, we find an exact equivalence between a class of BPS NN = 2 superconformal blocks and Virasoro conformal blocks in two dimensions, and an upper bound on the four-point functions of operators of sufficiently low scaling dimension in three and four dimensional CFTs.

Item Type:Article
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URLURL TypeDescription Paper
Lin, Ying-Hsuan0000-0001-8904-1287
Shao, Shu-Heng0000-0003-1294-2786
Simmons-Duffin, David0000-0002-2937-9515
Wang, Yifan0000-0001-9965-9777
Additional Information:© 2017 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: April 8, 2017. Accepted: May 13, 2017. Published: May 23, 2017. We would like to thank Chris Beem, Clay Córdova, Thomas Dumitrescu, Matthew Headrick, Christoph Keller, Petr Kravchuk, Sarah Harrison, Juan Maldacena, Hirosi Ooguri, Nati Seiberg, Steve Shenker, Cumrun Vafa, Shing-Tung Yau, and Alexander Zhiboedov for discussions. We would like to thank the workshop "From Scattering Amplitudes to the Conformal Bootstrap" at Aspen Center for Physics, the Simons Summer Workshop in Mathematics and Physics 2015, and the workshop Amplitudes in Asia 2015, for hospitality during the course of this work. DSD is supported by DOE grant DE-SC0009988 and a William D. Loughlin Membership at the Institute for Advanced Study. YW is supported in part by the U.S. Department of Energy under grant Contract Number DE-SC00012567. XY is supported by a Simons Investigator Award from the Simons Foundation, and in part by DOE grant DE-FG02-91ER40654.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0009988
Institute for Advanced StudyUNSPECIFIED
Department of Energy (DOE)DE-SC00012567
Simons FoundationUNSPECIFIED
Department of Energy (DOE)DE-FG02-91ER40654
Subject Keywords:Conformal Field Theory, Extended Supersymmetry, Field Theories in Lower Dimensions
Issue or Number:5
Record Number:CaltechAUTHORS:20170816-083440765
Persistent URL:
Official Citation:Lin, YH., Shao, SH., Simmons-Duffin, D. et al. J. High Energ. Phys. (2017) 2017: 126.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80465
Deposited By: Ruth Sustaita
Deposited On:16 Aug 2017 16:00
Last Modified:03 Oct 2019 18:31

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