S-duality, triangle groups and modular anomalies in \( \mathcal{N}=2 \) SQCD

  • S. K. Ashok
  • E. Dell’Aquila
  • A. Lerda
  • M. Raman
Open Access
Regular Article - Theoretical Physics

Abstract

We study \( \mathcal{N}=2 \) superconformal theories with gauge group SU(N ) and 2N fundamental flavours in a locus of the Coulomb branch with a \( {\mathbb{Z}}_N \) symmetry. In this special vacuum, we calculate the prepotential, the dual periods and the period matrix

using equivariant localization. When the flavors are massless, we find that the period matrix is completely specified by \( \left[\frac{N}{2}\right] \) effective couplings. On each of these, we show that the S-duality group acts as a generalized triangle group and that its hauptmodul can be used to write a non-perturbatively exact relation between each effective coupling and the bare one. For N = 2, 3, 4 and 6, the generalized triangle group is an arithmetic Hecke group which contains a subgroup that is also a congruence subgroup of the modular group \( \mathrm{P}\mathrm{S}\mathrm{L}\left(2,\mathbb{Z}\right) \). For these cases, we introduce mass deformations that respect the symmetries of the special vacuum and show that the constraints arising from S-duality make it possible to resum the instanton contributions to the period matrix in terms of meromorphic modular forms which solve modular anomaly equations.

Keywords

Supersymmetry and Duality Extended Supersymmetry Supersymmetric gauge theory Solitons Monopoles and Instantons 

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) 2016

Authors and Affiliations

  • S. K. Ashok
    • 1
  • E. Dell’Aquila
    • 1
  • A. Lerda
    • 2
  • M. Raman
    • 1
  1. 1.Institute of Mathematical Sciences, C.I.T. CampusChennaiIndia
  2. 2.Università del Piemonte Orientale, Dipartimento di Scienze e Innovazione Tecnologica, and INFN — Gruppo Collegato di Alessandria, Sezione di TorinoAlessandriaItaly

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