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Published June 2018 | Published + Submitted
Journal Article Open

Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters


We use Coulomb branch indices of Argyres-Douglas theories on S1×L(k,1) to quantize moduli spaces M_H of wild/irregular Hitchin systems. In particular, we obtain formulae for the "wild Hitchin characters" -- the graded dimensions of the Hilbert spaces from quantization -- for four infinite families of M_H, giving access to many interesting geometric and topological data of these moduli spaces. We observe that the wild Hitchin characters can always be written as a sum over fixed points in M_H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform STkS in certain two-dimensional chiral algebras. Although naturally fitting into the geometric Langlands program, the appearance of chiral algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.

Additional Information

© 2018 The Authors. 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: May 28, 2017. Accepted: January 9, 2018. Published: January 30, 2018. We thank Jørgen E. Andersen, Tomoyuki Arakawa, Chris Beem, Matthew Buican, Clay Córdova, Mykola Dedushenko, Davide Gaiotto, Tamás Hausel, Lotte Hollands, Victor Kac, Can Kozçaz, Conan Leung, Leonardo Rastelli, Shamil Shakirov, Shu-Heng Shao, Jaewon Song, Richard Wentworth, Dan Xie, Shing-Tung Yau and Matthew Young for helpful discussion. We would especially like to thank Philip Boalch, Sergei Gukov, Andrew Neitzke and Steve Rayan for reading our draft and offering their helpful comments, and Thomas Creutzig for sharing his notes as well as extensive communication and discussion. We are grateful for the organizers of the Simons Summer Workshop 2016, "RTG Workshop on the Geometry and Physics of Higgs bundles" held in University of Illinois at Chicago, and "exact operator algebras for superconformal field theories workshop" held at the Perimeter Institute for Theoretical Physics for the hospitality. DP and KY are supported by the DOE Grant DE-SC0011632, the Walter Burke Institute for Theoretical Physics. Additionally, the work of DP is also supported by the center of excellence grant "Center for Quantum Geometry of Moduli Space" from the Danish National Research Foundation (DNRF95). WY is supported by the Center for Mathematical Sciences and Applications at Harvard University.

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Published - 10.1007_2FJHEP01_2018_150.pdf

Submitted - 1701.08782v1.pdf


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