Proofs of Two Conjectures Related to the Thermodynamic Bethe Ansatz

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 exp(-u(theta)-u(theta'))/cosh[(1/2)(theta-theta')]

16 pages, LaTeX file, no figures. Revision has minor changes

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• Fredholm Determinants, Differential Equations and Matrix Models
• A New Supersymmetric Index
• Painleve III and 2D Polymers
• N=2 Supersymmetry, Painleve III and Exact Scaling Functions in 2D Polymers

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