Journal of High Energy Physics

, 2016:20 | Cite as

Chiral observables and S-duality in \( \mathcal{N} \) = 2 U(N ) gauge theories

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

Abstract

We study \( \mathcal{N} \) = 2 theories with gauge group U(N ) and use equivariant localization to calculate the quantum expectation values of the simplest chiral ring elements. These are expressed as an expansion in the mass of the adjoint hypermultiplet, with coefficients given by quasi-modular forms of the S-duality group. Under the action of this group, we construct combinations of chiral ring elements that transform as modular forms of definite weight. As an independent check, we confirm these results by comparing the spectral curves of the associated Hitchin system and the elliptic Calogero-Moser system. We also propose an exact and compact expression for the 1-instanton contribution to the expectation value of the chiral ring elements.

Keywords

Extended Supersymmetry Supersymmetric gauge theory Supersymmetry and Duality 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
  • M. Billò
    • 2
  • E. Dell’Aquila
    • 1
  • M. Frau
    • 2
  • A. Lerda
    • 3
  • M. Moskovic
    • 2
  • M. Raman
    • 1
  1. 1.Institute of Mathematical SciencesChennaiIndia
  2. 2.Università di Torino, Dipartimento di Fisica and I.N.F.N. - sezione di TorinoTorinoItaly
  3. 3.Università del Piemonte Orientale, Dipartimento di Scienze e Innovazione Tecnologica, and I.N.F.N. - sezione di TorinoTorinoItaly

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