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Chiral algebra, localization, modularity, surface defects, and all that

Dedushenko, Mykola and Fluder, Martin (2020) Chiral algebra, localization, modularity, surface defects, and all that. Journal of Mathematical Physics, 61 (9). Art. No. 092302. ISSN 0022-2488.

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We study the 2D vertex operator algebra (VOA) construction in 4D N=2 superconformal field theories on S³ × S¹, focusing on both old puzzles and new observations. The VOA lives on a two-torus T²⊂S³×S¹, it is 1/2Z-graded, and this torus is equipped with the natural choice of spin structure (1,0) for the Z+1/2-graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserves the VOA, we find that it admits discrete deformations, which allows access to the remaining spin structures (1,1), (0,1), and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle and the two-point functions and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the T-transformation acts on our four partition functions and lifts to a large diffeomorphism on S³ × S¹. More interestingly, we generalize the four partition functions on the torus to an infinite family labeled by both the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the S-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the Ω-background.

Item Type:Article
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URLURL TypeDescription Paper
Dedushenko, Mykola0000-0002-9273-7602
Fluder, Martin0000-0002-0780-8550
Additional Information:© 2020 Published under license by AIP Publishing. Submitted: 27 January 2020; Accepted: 17 August 2020; Published Online: 11 September 2020. We thank Thomas T. Dumitrescu, Sergei Gukov, Shu-Heng Shao, Nikita Sopenko, Lev Spodyneiko, and Yifan Wang for discussions and correspondence. M.D. was supported by the Walter Burke Institute for Theoretical Physics and the U.S. Department of Energy, Office of Science, Office of High Energy Physics (Award No. de-sc0011632) as well as the Sherman Fairchild Foundation. M.F. was partially supported by the JSPS Grants-in-Aid for Scientific Research Wakate(A) (Grant No. 17H04837), the WPI Initiative, MEXT, Japan, at IPMU, the University of Tokyo, the David and Ellen Lee Postdoctoral Scholarship, and the U.S. Department of Energy, Office of Science, Office of High Energy Physics (Award No. de-sc0011632).
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Sherman Fairchild FoundationUNSPECIFIED
Japan Society for the Promotion of Science (JSPS)17H04837
Ministry of Education, Culture, Sports, Science and Technology (MEXT)UNSPECIFIED
David and Ellen Lee Postdoctoral ScholarshipUNSPECIFIED
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Issue or Number:9
Record Number:CaltechAUTHORS:20190408-145734688
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Official Citation:Chiral algebra, localization, modularity, surface defects, and all that. Mykola Dedushenko and Martin Fluder. Journal of Mathematical Physics 61:9; doi: 10.1063/5.000266
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94572
Deposited By: Joy Painter
Deposited On:08 Apr 2019 22:52
Last Modified:11 Sep 2020 17:52

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