Hitchin systems, N=2 gauge theories and W-gravity

Details Hitchin systems, N=2 gauge theories and W-gravity Hitchin systems, N=2 gauge theories and W-gravity

2009-09-22

arxiv.org/abs/0909.4031v3

Physics

High Energy Physics

High Energy Physics - Theory

1 + 9 pages; v.2 refs and comments added; v3 version to appear on PLB

Scientific paper

We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N=2 superconformal gauge theories in four dimensions. We find that A_{N-1} Toda field theory is the simplest two-dimensional conformal field theory quantizing the moduli of N M5-branes wrapped on a Riemann surface. This leads us to identify chiral operators of the N=2 gauge theories with W-algebra currents. As a check of this correspondence we study some relevant OPE's obtaining that Nekrasov's partition function satisfies W-geometry constraints.

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