Journal of High Energy Physics

, 2011:117 | Cite as

Instantons and 2d superconformal field theory

Article

Abstract

A recently proposed correspondence between 4-dimensional \( \mathcal{N} = 2 \) SUSY SU(k) gauge theories on \( {{{{\mathbb{R}^4}}} \left/ {{{\mathbb{Z}_m}}} \right.} \) and SU(k) Toda-like theories with Zm parafermionic symmetry is used to construct four-point \( \mathcal{N} = 1 \) super Liouville conformal block, which corresponds to the particular case k = m = 2.

The construction is based on the conjectural relation between moduli spaces of SU(2) instantons on \( {{{{\mathbb{R}^4}}} \left/ {{{\mathbb{Z}_2}}} \right.} \) and algebras like \( \widehat{\text{gl}} {(2)_2} \times \mathcal{N}\mathcal{S}\mathcal{R} \). This conjecture is confirmed by checking the coincidence of number of fixed points on such instanton moduli space with given instanton number N and dimension of subspace degree N in the representation of such algebra.

Keywords

Conformal and W Symmetry Supersymmetric gauge theory 

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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRASChernogolovkaRussia
  2. 2.Theoretical Department, Lebedev Physical InstituteRASMoscowRussia
  3. 3.Independent University of MoscowMoscowRussia

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