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Elliptic genera of 2d (0,2) gauge theories from brane brick models

  • Sebastian Franco
  • Dongwook Ghim
  • Sangmin Lee
  • Rak-Kyeong Seong
Open Access
Regular Article - Theoretical Physics

Abstract

We compute the elliptic genus of abelian 2d (0, 2) gauge theories corresponding to brane brick models. These theories are worldvolume theories on a single D1-brane probing a toric Calabi-Yau 4-fold singularity. We identify a match with the elliptic genus of the non-linear sigma model on the same Calabi-Yau background, which is computed using a new localization formula. The matching implies that the quantum effects do not drastically alter the correspondence between the geometry and the 2d (0, 2) gauge theory. In theories whose matter sector suffers from abelian gauge anomaly, we propose an ansatz for an anomaly cancelling term in the integral formula for the elliptic genus. We provide an example in which two brane brick models related to each other by Gadde-Gukov-Putrov triality give the same elliptic genus.

Keywords

Conformal Field Theory D-branes Duality in Gauge Field Theories Supersymmetry and Duality 

Notes

Open Access

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.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Sebastian Franco
    • 1
    • 2
  • Dongwook Ghim
    • 3
  • Sangmin Lee
    • 3
    • 4
    • 5
  • Rak-Kyeong Seong
    • 6
  1. 1.Physics DepartmentThe City College of the CUNYNew YorkU.S.A.
  2. 2.The Graduate School and University CenterThe City University of New YorkNew YorkU.S.A.
  3. 3.Department of Physics and AstronomySeoul National UniversitySeoulKorea
  4. 4.Center for Theoretical PhysicsSeoul National UniversitySeoulKorea
  5. 5.College of Liberal StudiesSeoul National UniversitySeoulKorea
  6. 6.Department of Physics and AstronomyUppsala UniversityUppsalaSweden

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