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Title: Dirac spectrum and chiral condensate for QCD at fixed θ angle

Journal Article · · Physical Review. D.
; ;

We analyze the mass dependence of the chiral condensate for QCD at nonzero θ angle and find that in general the discontinuity of the chiral condensate is not on the support of the Dirac spectrum. To understand this behavior we decompose the spectral density and the chiral condensate into contributions from the zero modes, the quenched part, and a remainder which is sensitive to the fermion determinant and is referred to as the dynamical part. We obtain general formulas for the contributions of the zero modes. Expressions for the quenched part, valid for an arbitrary number of flavors, and for the dynamical part, valid for one and two flavors, are derived in the microscopic domain of QCD. We find that at nonzero θ angle the quenched and dynamical parts of the Dirac spectral density are strongly oscillating with an amplitude that increases exponentially with the volume V and a period of order of 1/V. The quenched part of the chiral condensate becomes exponentially large at θ ≠ 0 , but this divergence is canceled by the contribution from the zero modes. The oscillatory behavior of the dynamical part of the density is essential for moving the discontinuity of the chiral condensate away from the support of the Dirac spectrum. As important by-products of this work we obtain analytical expressions for the microscopic spectral density of the Dirac operator at nonzero θ angle for both one- and two-flavor QCD with nonzero quark masses.

Research Organization:
State Univ. of New York (SUNY), Stony Brook, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
FG02-88ER40388
OSTI ID:
1509927
Alternate ID(s):
OSTI ID: 1610130
Journal Information:
Physical Review. D., Journal Name: Physical Review. D. Vol. 99 Journal Issue: 7; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

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Figures / Tables (12)

FIG 1(p. 3)figure FIG 1
FIG. 2(p. 4)figure FIG. 2
FIG. 4(p. 4)figure FIG. 4
FIG. 5(p. 8)figure FIG. 5
FIG. 6(p. 9)figure FIG. 6
FIG. 7(p. 10)figure FIG. 7
FIG. 8(p. 12)figure FIG. 8
FIG. 9(p. 13)figure FIG. 9
FIG. 10(p. 14)figure FIG. 10
FIG. 11(p. 15)figure FIG. 11
FIG. 12(p. 15)figure FIG. 12
FIG. 13(p. 16)figure FIG. 13

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
astronomy & astrophysics
physics
chiral perturbation theory
nonperturbative effects in field theory
quantum chromodynamics
spontaneous symmetry breaking