3d N=4 Bootstrap and Mirror Symmetry
Chi-Ming Chang, Martin Fluder, Ying-Hsuan Lin, Shu-Heng Shao, Yifan Wang
SciPost Phys. 10, 097 (2021) · published 30 April 2021
- doi: 10.21468/SciPostPhys.10.4.097
- Submissions/Reports
Abstract
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.
Cited by 9
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 2 Chi-Ming Chang,
- 3 4 5 Martin Fluder,
- 3 6 Ying-Hsuan Lin,
- 7 Shu-Heng Shao,
- 4 8 Yifan Wang
- 1 Tsinghua University [THU]
- 2 University of California, Davis [UCD]
- 3 Walter Burke Institute for Theoretical Physics
- 4 Princeton University
- 5 東京大学 / University of Tokyo [UT]
- 6 Hsinchu County Environmental Protection Bureau
- 7 Institute for Advanced Study [IAS]
- 8 Harvard University
- 日本学術振興会 / Japan Society for the Promotion of Science [JSPS]
- Ministry of Research and Innovation (Canada, Ontario, Min Res&Innov) (through Organization: Ministry of Research, Innovation and Science - Ontario [MRIS])
- National Science Foundation [NSF]
- Scuola Normale Superiore (through Organization: Scuola Normale Superiore di Pisa)
- Sherman Fairchild Foundation
- Simons Foundation
- United States Department of Energy [DOE]