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arXiv · 0710.0376

Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential

Francesco Basile·Gernot Akemann
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Abstract

We prove that QCD in the epsilon-regime of chiral Perturbation Theory is equivalent to chiral Random Matrix Theory for zero and both non-zero real and imaginary chemical potential mu. To this aim we prove a theorem that relates integrals over fermionic and bosonic variables to super-Hermitian or super-Unitary groups also called superbosonization. Our findings extend previous results for the equivalence of the partition functions, spectral densities and the quenched two-point densities. We can show that all k-point density correlation functions agree in both theories for an arbitrary number of quark flavors, for either mu=0 or mu=/=0 taking real or imaginary values. This implies the equivalence for all individual k-th eigenvalue distributions which are particularly useful to determine low energy constants from Lattice QCD with chiral fermions.

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Francesco Basile, Gernot Akemann. 2007-12-13. Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential. https://doi.org/10.1088/1126-6708%2F2007%2F12%2F043

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