QCD, Wick's Theorem for KdV $τ$-functions and the String Equation

Details QCD, Wick's Theorem for KdV $τ$-functions and the String Equation QCD, Wick's Theorem for KdV $τ$-functions and the String Equation

2001-05-17

arxiv.org/abs/hep-th/0105169v2

Phys.Lett. B514 (2001) 293-298

Physics

High Energy Physics

High Energy Physics - Theory

7 pages LaTex. Corrections to grant numbers only for administering bureaucrats

Scientific paper

10.1016/S0370-2693(01)00829-2

Two consistency conditions for partition functions established by Akemann and Dam-gaard in their studies of the fermionic mass dependence of the QCD partition function at low energy ({\it a la} Leutwiller-Smilga-Verbaarschot) are interpreted in terms of integrable hierarchies. Their algebraic relation is shown to be a consequence of Wick's theorem for 2d fermionic correlators (Hirota identities) in the special case of the 2-reductions of the KP hierarchy (that is KdV/mKdV). The consistency condition involving derivatives is an incarnation of the string equation associated with the particular matrix model (the particular kind of the Kac-Schwarz operator).

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