On non-conformal limit of the AGT relations

By A. Marshakov, A. Mironov, A. Morozov. 2009

177 citations recorded by the source corpus.

Abstract The Seiberg–Witten prepotentials for N = 2 SUSY gauge theories with N f 2 N c fundamental multiplets are obtained from conformal N f = 2 N c theory by decoupling 2 N c − N f multiplets of heavy matter. This procedure can be lifted to the level of Nekrasov functions with arbitrary background parameters ϵ 1 and ϵ 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. 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ee699aa4d3af4b98a573e98504bbd40c2c2a25b6

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In Astronomy and Astrophysics

1. K. Maruyoshi
2. Yuji Tachikawa
3. G. Bonelli
4. A. Tanzini
5. H. Kanno
6. Dan Xie

In Nuclear and High Energy Physics

1. K. Maruyoshi
2. G. Bonelli
3. A. Tanzini
4. Yuji Tachikawa
5. R. Poghossian
6. A. Morozov
7. A. Mironov
8. H. Kanno

Citations in the corpus

• Instanton counting with a surface operator and the chain-saw quiver (2011, background): “In particular, the partition function of the pure SU(N) gauge theory is given by the norm of a coherent state in the Verma module [8, 9, 10].”
• Five-dimensional AGT conjecture and the deformed Virasoro algebra (2009, unknown): “This surprising conjecture has been extended to asymptotic-free cases [2, 3] and to SU(n)-gauge/Wn-CFT [4, 5].”
• Recursion relations in CFT and N=2 SYM theory (2009, background): “Contents”
• Nekrasov functions and exact Bohr-Sommerfeld integrals (2009, background): “four-fundamentals AGT formula [2, 5], see [6, 14 ] or, alternatively, as the large-M limit of the adjoint AGT formula, associated with the toric 1-point function [22]”
• How instanton combinatorics solves Painlevé VI, V and IIIs (2013, background): “The corresponding Nekrasov functions are related to irregular conformal blocks [25, 26, 39].”
• The Quiver Matrix Model and 2d-4d Conformal Connection (2009, background): “These are followed by a number of extensive checks and pieces of supporting evidence [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36].”
• Wild quiver gauge theories (2011, background): “Equivalently, this state can be written as [45]”