On AGT relation in the case of U(3)

Mironov, A.; Morozov, A.

doi:10.1016/j.nuclphysb.2009.09.011

On AGT relation in the case of U(3)

A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Morozov
(
- Moscow, ITEP
)

Aug, 2009

30 pages

Published in:

Nucl.Phys.B 825 (2010) 1-37

e-Print:

0908.2569 [hep-th]

DOI:

10.1016/j.nuclphysb.2009.09.011

Report number:

FIAN-TD-16-09,
ITEP-TH-32-09

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Abstract: (Elsevier)

We consider the AGT relation (Alday et al., 2009 [1] ), 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.

Note:

30 pages

algebra: Virasoro
group: U(3)
central charge
algebra: W(3)
field theory: conformal
n-point function: 3
Verma module
deformation
determinant
correlation function

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