Supersymmetric Quenching of the Toda Lattice Equation

Details Supersymmetric Quenching of the Toda Lattice Equation Supersymmetric Quenching of the Toda Lattice Equation

2004-02-23

arxiv.org/abs/hep-th/0402177v1

Nucl.Phys. B695 (2004) 84-102

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1016/j.nuclphysb.2004.06.022

The average of the ratio of powers of the spectral determinants of the Dirac operator in the $\epsilon$-regime of QCD is shown to satisfy a Toda lattice equation. The quenched limit of this Toda lattice equation is obtained using the supersymmetric method. This super symmetric approach is then shown to be equivalent to taking the replica limit of the Toda lattice equation. Among other, the factorization of the microscopic spectral correlation functions of the QCD Dirac operator into fermionic and bosonic partition functions follows naturally from both approaches. While the replica approach relies on an analytic continuation in the number of flavors no such assumptions are made in the present approach where the numbers of flavors in the Toda lattice equation are strictly integer.

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