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On non-conformal limit of the AGT relations · Around

2009

On non-conformal limit of the AGT relations

Marshakov, A., Mironov, A., Morozov, A.

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The Seiberg-Witten prepotentials for N=2 SUSY gauge theories with N_f<2N_c fundamental multiplets are obtained from conformal N_f=2N_c theory by decoupling 2N_c-N_f multiplets of heavy matter.

This procedure can be lifted to the level of Nekrasov functions with arbitrary background parameters epsilon_1 and epsilon_2.
The AGT relations imply that similar limit exists for conformal blocks (or, for generic N_c>2, for the blocks in conformal theories with W_{N_c} chiral algebra).
We consider the limit of the four-point function explicitly in the Virasoro case of N_c=2, by bringing the dimensions of external states to infinity.

Built on

N.Seiberg and E.Witten, Nucl.Phys., B426
Original
1996
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R.Flume and R.Pogossian, Int.J.Mod.Phys. A18
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N.Nekrasov, Adv.Theor.Math.Phys. 7
2004
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D. Bellisai, F. Fucito, A. Tanzini and G. Travaglini, Phys. Lett. B 480
2004
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Then

E.Witten, Nucl.Phys., B500
Original
2009
Closest in time.
A.Belavin, A.Polyakov, A.Zamolodchikov, Nucl.Phys., B241
2009
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Andrey Mironov, Sergey Mironov, Alexei Morozov and Andrey Morozov, arXiv:0908.2064
Original
2064
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