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Elliptic Genera of Two-Dimensional \({\mathcal{N} = 2}\) Gauge Theories with Rank-One Gauge Groups

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Abstract

We compute the elliptic genera of two-dimensional \({\mathcal{N} = (2, 2)}\) and \({\mathcal{N} = (0, 2)}\) -gauged linear sigma models via supersymmetric localization, for rank-one gauge groups. The elliptic genus is expressed as a sum over residues of a meromorphic function whose argument is the holonomy of the gauge field along both the spatial and the temporal directions of the torus. We illustrate our formulas by a few examples including the quintic Calabi–Yau, \({\mathcal{N} = (2, 2)}\) SU(2) and O(2) gauge theories coupled to N fundamental chiral multiplets, and a geometric \({\mathcal{N} = (0, 2)}\) model.

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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, 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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Benini, F., Eager, R., Hori, K. et al. Elliptic Genera of Two-Dimensional \({\mathcal{N} = 2}\) Gauge Theories with Rank-One Gauge Groups. Lett Math Phys 104, 465–493 (2014). https://doi.org/10.1007/s11005-013-0673-y

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