Fredholm determinants and the mKdV/sinh-Gordon hierarchies

Abstract

For a particular class of integral operators $K$ we show that the quantity \[\ph:=\log \det (I+K)-\log \det (I-K)\] satisfies both the integrated mKdV hierarchy and the sinh-Gordon hierarchy. This proves a conjecture of Zamolodchikov.

11 pages, LaTeX file, no figures

References in corpus (3)

• Fredholm Determinants, Differential Equations and Matrix Models
• Painleve III and 2D Polymers
• Differential Equations for Sine-Gordon Correlation Functions at the Free Fermion Point

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