Abstract
We prove that the solution to a pair of nonlinear integral equations arising in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent kernel of the linear integral operator with kernel
.
Similar content being viewed by others
References
Cecotti, S., Vafa, C.: Topological-anti-topological fusion. Nucl. Phys.B367, 359–461 (1991); Ising model andN=2 supersymmetric theories. Commun. Math. Phys.157, 139–178 (1993)
Cecotti, S., Fendley, P., Intriligator, K., Vafa, C.: A new supersymmetric index. Nucl. Phys.B386, 405–452 (1992)
Fendley, P., Saleur, H.:N=2 supersymmetry, Painlevé III and exact scaling functions in 2D polymers. Nucl. Phys.B388, 609–626 (1992)
Its, A.R., Izergin, A.G., Korepin, V.E., Slavnov, N.A.: Differential equations for quantum correlation functions. Int. J. Mod. PhysicsB4, 1003–1037 (1990)
Klassen, T.R., Melzer, E.: The thermodynamics of purely elastic scattering theories and conformal perturbation theory. Nucl. Phys.B350, 635–689 (1991)
McCoy, B.M., Tracy, C.A., Wu, T.T.: Painlevé functions of the third kind. J. Math. Phys.18, 1058–1092 (1977)
Rudin, W.: Real and Complex Analysis. 3rd ed. New York: McGraw-Hill, 1987
Tracy, C.A., Widom, H.: Fredholm determinants, differential equations and matrix models. Commun. Math. Phys.163, 33–72 (1994)
Tracy, C.A., Widom, H.: Systems of partial differential equations for a class of operator determinants. Operator Theory: Adv. and Appls.78, 381–388 (1995)
Tracy, C.A., Widom, H.: Fredholm determinants and the mKdV/sinh-Gordon hierarchies. Commun. Math. Phys.
Yang, C.N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. J. Math. Phys.10, 1115–1122 (1969)
Zamolodchikov, Al.B.: Thermodynamic Bethe Ansatz in relativistic models: Scaling 3-state Potts and Lee-Yang models. Nucl. Phys.B342, 695–720 (1990)
Zamolodchikov, Al.B.: Painlevé III and 2D polymers. Nucl. Phys.B432[FS], 427–456 (1994)
Author information
Authors and Affiliations
Additional information
Communicated by M. Jimbo
Rights and permissions
About this article
Cite this article
Tracy, C.A., Widom, H. Proofs of two conjectures related to the thermodynamic Bethe Ansatz. Commun.Math. Phys. 179, 667–680 (1996). https://doi.org/10.1007/BF02100102
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02100102