Abstract
A system of Bethe-Ansatz type equations, which specify a unique array of Young tableau responsible for the leading contribution to the Nekrasov partition function in the ϵ2 → 0 limit is derived. It is shown that the prepotential with generic ϵ1 is directly related to the (rescaled by ϵ2) number of total boxes of these Young tableau. Moreover, all the expectation values of the chiral fields \( \left\langle {{\text{tr}}{\phi^J}} \right\rangle \) are simple symmetric functions of their column lengths. An entire function whose zeros are determined by the column lengths is introduced. It is shown that this function satisfies a functional equation, closely resembling Baxter’s equation in 2d integrable models. This functional relation directly leads to a nice generalization of the equation defining Seiberg-Witten curve.
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References
G.W. Moore, N. Nekrasov and S. Shatashvili, Integrating over Higgs branches, Commun. Math. Phys. 209 (2000) 97 [hep-th/9712241] [SPIRES].
A. Lossev, N. Nekrasov and S.L. Shatashvili, Testing Seiberg-Witten solution, contribution to Cargese conference, June 1997, hep-th/9801061 [SPIRES].
N.A. Nekrasov, Seiberg-Witten Prepotential From Instanton Counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [SPIRES].
R. Flume and R. Poghossian, An algorithm for the microscopic evaluation of the coefficients of the Seiberg-Witten prepotential, Int. J. Mod. Phys. A 18 (2003) 2541 [hep-th/0208176] [SPIRES].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [SPIRES].
N.A. Nekrasov and S.L. Shatashvili, Quantization of Integrable Systems and Four Dimensional Gauge Theories, arXiv:0908.4052 [SPIRES].
N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, hep-th/0306238 [SPIRES].
N. Seiberg and E. Witten, Monopole Condensation, And Confinement In N = 2 Supersymmetric Yang-Mills Theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. B 430 (1994) 485] [hep-th/9407087] [SPIRES].
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [SPIRES].
A.S. Losev, A. Marshakov and N.A. Nekrasov, Small instantons, little strings and free fermions, hep-th/0302191 [SPIRES].
R. Flume, F. Fucito, J.F. Morales and R. Poghossian, Matone’s relation in the presence of gravitational couplings, JHEP 04 (2004) 008 [hep-th/0403057] [SPIRES].
M. Matone, Instantons and recursion relations in N = 2 SUSY gauge theory, Phys. Lett. B 357 (1995) 342 [hep-th/9506102] [SPIRES].
V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov, Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz, Commun. Math. Phys. 177 (1996) 381 [hep-th/9412229] [SPIRES].
C.-N. Yang and C.P. Yang, Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction, J. Math. Phys. 10 (1969) 1115 [SPIRES].
A.B. Zamolodchikov, Thermodynamic Bethe Ansatz in Relativistic Models: Scaling 3-state Potts and Lee-Yang Models, Nucl. Phys. B 342 (1990) 695 [SPIRES].
A.B. Zamolodchikov, On the thermodynamic Bethe ansatz equations for reflectionless ADE scattering theories, Phys. Lett. B 253 (1991) 391 [SPIRES].
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ArXiv ePrint: 1006.4822
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Poghossian, R. Deforming SW curve. J. High Energ. Phys. 2011, 33 (2011). https://doi.org/10.1007/JHEP04(2011)033
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DOI: https://doi.org/10.1007/JHEP04(2011)033