The Spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

Toublan, D.; Verbaarschot, J.J.M.

doi:10.1016/S0550-3213(99)00449-6

The Spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

Apr, 1999

27 pages

Published in:

Nucl.Phys.B 560 (1999) 259-282

e-Print:

hep-th/9904199 [hep-th]

DOI:

10.1016/S0550-3213(99)00449-6

Report number:

SUNY-NTG-99-8

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Abstract:

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For

N_f

flavors, the chiral flavor symmetry of these theories is spontaneously broken according to

SU(2N_f)\to Sp(2N_f)

and

SU(N_f)\to O(N_f)

, respectively, rather than the symmetry breaking pattern

SU(N_f) \times SU(N_f) \to SU(N_f)

for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain

\lambda \ll \Lambda_{\rm QCD}

by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at

\lambda = 0

. We also show that for

\lambda \ll 1/L^2 \Lambda_{QCD}

(with

L

the linear size of the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator.

Note:

27 pages Latex, corrected typos Report-no: SUNY-NTG-99/8

11.30.Rd
12.39.Fe
12.38.Lg
71.30.+h
QCD Dirac operator
Chiral random matrix theory
Partially quenched chiral perturbation theory
Microscopic spectral density
Valence quark mass dependence
quantum chromodynamics

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