On AGT relation in the case of U(3)

Details On AGT relation in the case of U(3) On AGT relation in the case of U(3)

2009-08-18

arxiv.org/abs/0908.2569v2

Nucl.Phys.B825:1-37,2010

Physics

High Energy Physics

High Energy Physics - Theory

30 pages

Scientific paper

10.1016/j.nuclphysb.2009.09.011

We consider the AGT relation, expressing conformal blocks for the Virasoro and W-algebras in terms of Nekrasov's special functions, in the simplest case of the 4-point functions for the first non-trivial W_3 algebra. The standard set of Nekrasov functions is sufficient only if additional null-vector restriction is imposed on a half of the external $W$-primaries and this is just the case when the conformal blocks are fully dictated by W-symmetry and do not depend on a particular model. Explicit checks confirm that the AGT relation survives in this restricted case, as expected.

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