Fredholm determinants and the mKdV/Sinh-Gordon hierarchies
Copyright policy )Fredholm determinants and the mKdV/Sinh-Gordon hierarchies
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
- University of California, Davis United States
- University of California United States
- University of California, Santa Cruz United States
High Energy Physics - Theory, conjecture of Zamolodchikov, correlation functions, Nonlinear Sciences - Exactly Solvable and Integrable Systems, hep-th, math-ph, Sinh-Gordon hierarchy, FOS: Physical sciences, Model quantum field theories, Mathematical Physics (math-ph), Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, 58F07, 35Q53, math.MP, KdV equations (Korteweg-de Vries equations), mKdV hierarchy, High Energy Physics - Theory (hep-th), Exactly Solvable and Integrable Systems (nlin.SI), solv-int, nlin.SI, Mathematical Physics, Fredholm determinants
High Energy Physics - Theory, conjecture of Zamolodchikov, correlation functions, Nonlinear Sciences - Exactly Solvable and Integrable Systems, hep-th, math-ph, Sinh-Gordon hierarchy, FOS: Physical sciences, Model quantum field theories, Mathematical Physics (math-ph), Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, 58F07, 35Q53, math.MP, KdV equations (Korteweg-de Vries equations), mKdV hierarchy, High Energy Physics - Theory (hep-th), Exactly Solvable and Integrable Systems (nlin.SI), solv-int, nlin.SI, Mathematical Physics, Fredholm determinants
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