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Superconformal index, BPS monodromy and chiral algebras

Cecotti, Sergio and Song, Jaewon and Vafa, Cumrun and Yan, Wenbin (2017) Superconformal index, BPS monodromy and chiral algebras. Journal of High Energy Physics, 2017 (11). Art. No. 013. ISSN 1029-8479.

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We show that specializations of the 4d N=2 superconformal index labeled by an integer N is given by Tr ℳ^N where ℳ is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras ANAN. This generalizes the recent results for the N = −1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on S^2× T^2 where we turn on 1/2N units of U(1)_r flux on S^2.

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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. Article funded by SCOAP3. Received: August 16, 2017; Accepted: October 16, 2017; Published: November 6, 2017. We thank T. Dumitrescu, S. Gukov, A. Kirillov, K. Lee, P. Putrov, L. Rastelli, V. Stylianou, Y. Tachikawa, and O. Warnaar for useful discussions. We wish to thank the hospitality of the Simons Center for Geometry and Physics where this work was initiated during the 2015 summer workshop in mathematics and physics. SC would also like to thank the Bershadsky Visiting Fellowship while visiting the Department of Physics at Harvard University. JS would also like to thank hospitality of the Department of Physics at Harvard University. The research of CV is supported in part by NSF grant PHY-1067976. The research of JS is supported by the US Department of Energy under UCSD's contract de-sc0009919. The research of WY is supported by the Center for Mathematical Sciences and Applications at Harvard University.
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Harvard UniversityUNSPECIFIED
Department of Energy (DOE)DE-SC0009919
Subject Keywords:Conformal Field Theory; Supersymmetric Gauge Theory
Issue or Number:11
Record Number:CaltechAUTHORS:20171113-135614634
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Official Citation:Cecotti, S., Song, J., Vafa, C. et al. J. High Energ. Phys. (2017) 2017: 13.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83157
Deposited By: Tony Diaz
Deposited On:14 Nov 2017 01:51
Last Modified:03 Oct 2019 19:03

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