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3d N=4 Bootstrap and Mirror Symmetry

Chang, Chi-Ming and Fluder, Martin and Lin, Ying-Hsuan and Shao, Shu-Heng and Wang, Yifan (2019) 3d N=4 Bootstrap and Mirror Symmetry. . (Unpublished)

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We investigate the non-BPS realm of 3d ${\cal N} = 4$ superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d ${\cal N} = 4$ theories such as mirror symmetry and a protected sector described by topological quantum mechanics (TQM). Supersymmetric localization allows for the exact determination of the conformal and flavor central charges, and the latter can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE data. We examine the implications of the $\mathbb{Z}_2$ mirror action for the SCFT single- and mixed-branch crossing equations for the moment map operators, and apply numerical bootstrap to obtain universal constraints on OPE data for given flavor symmetry groups. A key ingredient in applying the bootstrap analysis is the determination of the mixed-branch superconformal blocks. Among other results, we show that the simplest known self-mirror theory with $SU(2) \times SU(2)$ flavor symmetry saturates our bootstrap bounds, which allows us to extract the non-BPS data and examine the self-mirror $\mathbb{Z}_2$ symmetry thereof.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Fluder, Martin0000-0002-0780-8550
Lin, Ying-Hsuan0000-0001-8904-1287
Shao, Shu-Heng0000-0003-1294-2786
Wang, Yifan0000-0001-9965-9777
Additional Information:We are grateful to Silviu Pufu for interesting comments on the draft. The computations in this paper are performed on the Helios computing cluster supported by the School of Natural Sciences Computing Staff at the Institute for Advanced Study. C.C. is supported in part by the U.S. Department of Energy grant DE-SC0009999. The work of M.F. is supported by an SNS fellowship P400P2-180740, the Princeton physics department, the JSPS Grant-In-Aid for Scientific Research Wakate(A) 17H04837, the WPI Initiative, MEXT, Japan at IPMU, the University of Tokyo, and the David and Ellen Lee Postdoctoral Scholarship. Y.L. is supported by the Sherman Fairchild Foundation, and both M.F. and Y.L. by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. The work of S.H.S. is supported by the National Science Foundation grant PHY-1606531, the Roger Dashen Membership, and a grant from the Simons Foundation/SFARI (651444, NS). The work of Y.W. is supported in part by the US NSF under Grant No. PHY-1620059 and by the Simons Foundation Grant No. 488653. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research and Innovation. C.C., M.F., S.H.S. and Y.W. thank the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611, for hospitality during the finishing stages of this paper.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
David and Ellen Lee Postdoctoral ScholarshipUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Simons Foundation651444
Department of Innovation, Science and Economic Development (Canada)UNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
Princeton UniversityUNSPECIFIED
Swiss National Science Foundation (SNSF)P400P2-180740
Japan Society for the Promotion of Science (JSPS)17H04837
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Record Number:CaltechAUTHORS:20191028-152246947
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99509
Deposited By: Joy Painter
Deposited On:28 Oct 2019 23:05
Last Modified:07 Feb 2020 17:37

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