gauge theories on toric singularities, blow-up formulae and W-algebrae View Full Text


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Article Info

DATE

2013-01-02

AUTHORS

Giulio Bonelli, Kazunobu Maruyoshi, Alessandro Tanzini, Futoshi Yagi

ABSTRACT

We compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{{{{\mathbb{C}}^2}}} \left/ {\varGamma } \right.} $\end{document} in terms of blow-up formulae. We discuss the expansion of the partition function in the ϵ1, ϵ2 → 0 limit along with its modular properties and how to derive them from the M-theory perspective. On the two-dimensional conformal field theory side, our results can be interpreted in terms of representations of the direct sum of Heisenberg plus WN-algebrae with suitable central charges, which can be computed from the fan of the resolved toric variety. We provide a check of this correspondence by computing the central charge of the two-dimensional theory from the anomaly polynomial of M5-brane theory. Upon using the AGT correspondence our results provide a candidate for the conformal blocks and three-point functions of a class of the two-dimensional CFTs which includes parafermionic theories. More... »

PAGES

14

References to SciGraph publications

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  • 2012-02-13. Parafermionic Liouville field theory and instantons on ALE spaces in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-08-16. Instantons on ALE spaces and super Liouville conformal field theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-04-08. Poincaré Polynomial of Moduli Spaces of Framed Sheaves on (Stacky) Hirzebruch Surfaces in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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