Letters in Mathematical Physics

, Volume 101, Issue 1, pp 103–124

Gauge Theories on ALE Space and Super Liouville Correlation Functions

  • Giulio Bonelli
  • Kazunobu Maruyoshi
  • Alessandro Tanzini
Article

DOI: 10.1007/s11005-012-0553-x

Cite this article as:
Bonelli, G., Maruyoshi, K. & Tanzini, A. Lett Math Phys (2012) 101: 103. doi:10.1007/s11005-012-0553-x

Abstract

We present a relation between \({\mathcal{N}=2}\) quiver gauge theories on the ALE space \({\mathcal{O}_{\mathbb{P}^1}(-2)}\) and correlators of \({\mathcal{N}=1}\) super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the \({\mathcal{N}=2^*}\) instanton partition function is given by the product of the character of \({\widehat{SU}(2)_2}\) times the super Virasoro conformal block on the torus with one puncture. Moreover, we match the perturbative gauge theory contribution with super Liouville three-point functions.

Mathematics Subject Classification

81T4081T60

Keywords

conformal field theorysupersymmetric gauge theory

Copyright information

© Springer 2012

Authors and Affiliations

  • Giulio Bonelli
    • 1
    • 2
    • 3
  • Kazunobu Maruyoshi
    • 1
    • 2
  • Alessandro Tanzini
    • 1
    • 2
  1. 1.International School of Advanced Studies (SISSA)TriesteItaly
  2. 2.INFN, Sezione di TriesteTriesteItaly
  3. 3.I.C.T.P.TriesteItaly