Random matrix model of QCD at finite density and the nature of the quenched limit

Details Random matrix model of QCD at finite density and the nature of the quenched limit Random matrix model of QCD at finite density and the nature of the quenched limit

1996-04-04

arxiv.org/abs/hep-lat/9604003v2

Phys.Rev.Lett. 76 (1996) 4472-4475

Physics

High Energy Physics

High Energy Physics - Lattice

9 pages, revtex3.0, 4 epsf figures. Packed by "uufiles" script. Revised version (PRL): minor changes

Scientific paper

10.1103/PhysRevLett.76.4472

We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential $\mu$. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails for $\mu\neq0$: we find that quenched QCD is not a simple $n\to0$ limit of QCD with $n$ quarks. It is the limit of a theory with $2n$ quarks: $n$ quarks with original action and $n$ quarks with conjugate action. The results agree with earlier studies of lattice QCD at $\mu\neq0$ and provide a simple analytical explanation of a long-standing puzzle.

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