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Elliptic Genera of 2d \({\mathcal{N}}\) = 2 Gauge Theories

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Abstract

We compute the elliptic genera of general two-dimensional \({\mathcal{N} = (2, 2)}\) and \({\mathcal{N} = (0, 2)}\) gauge theories. We find that the elliptic genus is given by the sum of Jeffrey–Kirwan residues of a meromorphic form, representing the one-loop determinant of fields, on the moduli space of flat connections on T 2. We give several examples illustrating our formula, with both Abelian and non-Abelian gauge groups, and discuss some dualities for U(k) and SU(k) theories. This paper is a sequel to the authors’ previous paper (Benini et al., Lett Math Phys 104:465–493, 2014).

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Authors and Affiliations

  1. Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, 11794, USA

    Francesco Benini

  2. Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba, 277-8583, Japan

    Richard Eager & Kentaro Hori

  3. Department of Physics, Faculty of Science, University of Tokyo, Bunkyo-ku, Tokyo, 133-0022, Japan

    Yuji Tachikawa

Authors
  1. Francesco Benini
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  2. Richard Eager
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  3. Kentaro Hori
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  4. Yuji Tachikawa
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Correspondence to Francesco Benini.

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Communicated by N. A. Nekrasov

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Benini, F., Eager, R., Hori, K. et al. Elliptic Genera of 2d \({\mathcal{N}}\) = 2 Gauge Theories. Commun. Math. Phys. 333, 1241–1286 (2015). https://doi.org/10.1007/s00220-014-2210-y

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