807 research outputs found
Comment on Dirac spectral sum rules for QCD_3
Recently Magnea hep-th/9907096 , hep-th/9912207 [Phys.Rev.D61, 056005 (2000);
Phys.Rev.D62, 016005 (2000)] claimed to have computed the first sum rules for
Dirac operators in 3D gauge theories from 0D non-linear sigma models. I point
out that these computations are incorrect, and that they contradict with the
exact results for the spectral densities unambiguously derived from random
matrix theory by Nagao and myself.Comment: REVTeX 3.1, 2 pages, no figure. (v2) redundant part removed,
conclusion unchange
Ratios of characteristic polynomials in complex matrix models
We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as their Cauchy transforms, generalizing previous expressions for real eigenvalues. We restrict ourselves to ratios of characteristic polynomials over their complex conjugate
Finding the Pion in the Chiral Random Matrix Vacuum
The existence of a Goldstone boson is demonstrated in chiral random matrix
theory. After determining the effective coupling and calculating the scalar and
pseudoscalar propagators, a random phase approximation summation reveals the
massless pion and massive sigma modes expected whenever chiral symmetry is
spontaneously broken.Comment: 3 pages, 1 figure, revte
Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential
In quantum chromodynamics (QCD) at nonzero chemical potential, the
eigenvalues of the Dirac operator are scattered in the complex plane. Can the
fluctuation properties of the Dirac spectrum be described by universal
predictions of non-Hermitian random matrix theory? We introduce an unfolding
procedure for complex eigenvalues and apply it to data from lattice QCD at
finite chemical potential to construct the nearest-neighbor spacing
distribution of adjacent eigenvalues in the complex plane. For intermediate
values of , we find agreement with predictions of the Ginibre ensemble of
random matrix theory, both in the confinement and in the deconfinement phase.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let
On the Phase Diagram of QCD
We analyze the phase diagram of QCD with two massless quark flavors in the
space of temperature, T, and chemical potential of the baryon charge, mu, using
available experimental knowledge of QCD, insights gained from various models,
as well as general and model independent arguments including continuity,
universality, and thermodynamic relations. A random matrix model is used to
describe the chiral symmetry restoration phase transition at finite T and mu.
In agreement with general arguments, this model predicts a tricritical point in
the T mu plane. Certain critical properties at such a point are universal and
can be relevant to heavy ion collision experiments.Comment: 21 pages, version to appear in Phys. Rev. D (2 references added
Quantum Chaos in Compact Lattice QED
Complete eigenvalue spectra of the staggered Dirac operator in quenched
compact QED are studied on and lattices. We
investigate the behavior of the nearest-neighbor spacing distribution as
a measure of the fluctuation properties of the eigenvalues in the strong
coupling and the Coulomb phase. In both phases we find agreement with the
Wigner surmise of the unitary ensemble of random-matrix theory indicating
quantum chaos. Combining this with previous results on QCD, we conjecture that
quite generally the non-linear couplings of quantum field theories lead to a
chaotic behavior of the eigenvalues of the Dirac operator.Comment: 11 pages, 4 figure
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