A(N-1) conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories

By N. Wyllard. 2009

642 citations recorded by the source corpus.

We propose a relation between correlation functions in the 2d A(N-1) conformal Toda theories and the Nekrasov instanton partition functions in certain conformal N = 2 SU(N) 4d quiver gauge theories. Our proposal generalises the recently uncovered relation between the Liouville theory and SU(2) quivers [1]. New features appear in the analysis that have no counterparts in the Liouville case.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/78e3bd45a832722591f9759204d74c6e128be7b5

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Citations in the corpus

Gauge Theories and Macdonald Polynomials (2011, methodology): “2 According to the celebrated AGT conjecture [7, 8, 9], the 4d partition functions on the Ω-background [10] and on S4 [11] are computed by Liouville/Toda theory on C.”
The Ω Deformed B-model for Rigid N = 2 Theories (2011, background): “It has been argued that for such theories, a correspondence exists to 2d AN−1 Toda theory [35].”
Gauge theory loop operators and Liouville theory (2009, methodology): “On the Riemann surface they involve conformal field theories with W-symmetry [13, 61].”
Chern-Simons theory and S-duality (2011, methodology): “One should replace Teichmüller theory with “higher” Teichmüller theory [25], and Liouville theory with an appropriate Toda CFT [4, 26].”
Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems (2009, neutral): “September 2009”
Bootstrapping the superconformal index with surface defects (2012, background): “Nekrasov’s instanton partition function for the 4d theory is conjecturally the same as a conformal block for the WN current algebra [20, 77].”
Seiberg-Witten theories on ellipsoids (2012, background): “They also led to a discovery of a surprising connection between SW theories and 2D Liouville or Toda conformal field theories, called AGT relation [10, 11].”
A& B model approaches to surface operators and Toda thoeries (2010, neutral): “20 25 v2 [ he p- th ] 1 5 A pr 2 01 Table of contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2”
The omega deformation, branes, integrability and Liouville theory (2010, background): “If SU(2) is replaced by another simply-laced group G, then [43, 44] the relevant objects are the conformal blocks of the corresponding Toda field theory.”