On non-conformal limit of the AGT relations
Sep, 2009
7 pages
Published in:
- Phys.Lett.B 682 (2009) 125-129
e-Print:
- 0909.2052 [hep-th]
Report number:
- FIAN-TD-19-09,
- ITEP-TH-41-09
View in:
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Abstract: (Elsevier)
The Seiberg–Witten prepotentials for N=2 SUSY gauge theories with Nf<2Nc fundamental multiplets are obtained from conformal Nf=2Nc theory by decoupling 2Nc−Nf multiplets of heavy matter. This procedure can be lifted to the level of Nekrasov functions with arbitrary background parameters ϵ1 and ϵ2 . The AGT relations imply that similar limit exists for conformal blocks (or, for generic Nc>2 , for the blocks in conformal theories with WNc chiral algebra). We consider the limit of the four-point function explicitly in the Virasoro case of Nc=2 , by bringing the dimensions of external states to infinity. The calculation is performed entirely in terms of representation theory for the Virasoro algebra and reproduces the answers conjectured in [D. Gaiotto, arXiv:0908.0307 ] with the help of the brane-compactification analysis and computer simulations. In this limit, the conformal block involving four external primaries, corresponding to the theory with vanishing beta-function, turns either into a 2-point or 3-point function, with certain coherent rather than primary external states.Note:
- 7 pages
- algebra: Virasoro
- gauge field theory: supersymmetry
- field theory: conformal
- n-point function: 4
- algebra: chiral
- prepotential
- gauge field theory: SU(N)
- fermion: flavor
- SU(2)
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