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Related papers: Dirac Operator Spectra from Finite-Volume Partitio…

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In the $\varepsilon$-regime of chiral perturbation theory the spectral correlations of the Euclidean QCD Dirac operator close to the origin can be computed using random matrix theory. To incorporate the effect of temperature, a random…

Mathematical Physics · Physics 2022-01-05 Gernot Akemann , Tim R. Würfel

Based on the exact relationship to Random Matrix Theory, we derive the probability distribution of the k-th smallest Dirac operator eigenvalue in the microscopic finite-volume scaling regime of QCD and related gauge theories.

High Energy Physics - Theory · Physics 2009-10-31 P. H. Damgaard , S. M. Nishigaki

The application of Random Matrix Theory to the Dirac operator of QCD yields predictions for the probability distributions of the lowest eigenvalues. We measured Dirac operator spectra using massless overlap fermions in quenched QCD at…

High Energy Physics - Lattice · Physics 2009-11-10 S. Shcheredin , W. Bietenholz , T. Chiarappa , K. Jansen , K. -I. Nagai

The zero momentum sectors in effective theories of three dimensional QCD coupled to pseudoreal (two colors) and real (adjoint) quarks in a classically parity-invariant manner have alternative descriptions in terms of orthogonal and…

High Energy Physics - Theory · Physics 2016-09-06 T. Nagao , S. M. Nishigaki

We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU($N_c$)…

High Energy Physics - Theory · Physics 2019-07-01 Sudhakantha Girmohanta , Thomas A. Ryttov , Robert Shrock

The low-lying spectrum of the Dirac operator is predicted to be universal, within three classes, depending on symmetry properties specified according to random matrix theory. The three universal classes are the orthogonal, unitary and…

High Energy Physics - Lattice · Physics 2009-10-31 Robert G. Edwards , Urs M. Heller , Rajamani Narayanan

The microscopic spectral correlations of the Dirac operator in Yang-Mills theories coupled to fermions in (2+1) dimensions can be related to three universality classes of Random Matrix Theory. In the microscopic limit the Orthogonal…

High Energy Physics - Theory · Physics 2009-10-31 Christian Hilmoine , Rune Niclasen

We consider half-line Dirac operators with operator data of Wigner-von Neumann type. If the data is a finite linear combination of Wigner-von Neumann functions, we show absence of singular continuous spectrum and provide an explicit set…

Spectral Theory · Mathematics 2021-09-29 Ethan Gwaltney

In the presence of a non-vanishing chemical potential the eigenvalues of the Dirac operator become complex. We calculate spectral correlation functions of complex eigenvalues using a random matrix model approach. Our results apply to…

High Energy Physics - Theory · Physics 2009-11-07 G. Akemann

We investigate the index of the Neuberger's Dirac operator in abelian gauge theories on finite lattices by numerically analyzing the spectrum of the hermitian Wilson-Dirac operator for a continuous family of gauge fields connecting…

High Energy Physics - Lattice · Physics 2009-10-31 T. Fujiwara

The properties of the spectrum of the overlap Dirac operator and their relation to random matrix theory are studied. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are…

High Energy Physics - Lattice · Physics 2015-06-25 Robert G. Edwards , Urs M. Heller , Joe Kiskis , Rajamani Narayanan

We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action…

High Energy Physics - Lattice · Physics 2009-10-31 F. Farchioni , I. Hip , C. B. Lang , M. Wohlgenannt

All microscopic correlation functions of the spectrum of the Hermitian Wilson Dirac operator with any number of flavors with equal masses are computed. In particular, we give explicit results for the spectral density in the physical case…

High Energy Physics - Lattice · Physics 2013-05-29 K. Splittorff , J. J. M. Verbaarschot

We compute the spectrum of SU(2) gauge theory with two, four or six Dirac fermions in the fundamental representation of the gauge group. We investigate the scaling of the meson masses as a function of the quark mass when approaching the…

High Energy Physics - Lattice · Physics 2018-06-20 Alessandro Amato , Viljami Leino , Kari Rummukainen , Kimmo Tuominen , Sara Tähtinen

We report tests and results from a new approach to the spectral density and the mode number distribution of the Dirac operator in lattice gauge theories. The algorithm generates the spectral density of the lattice Dirac operator as a…

High Energy Physics - Lattice · Physics 2016-05-27 Zoltan Fodor , Kieran Holland , Julius Kuti , Santanu Mondal , Daniel Nogradi , Chik Him Wong

We investigate the spectral properties of the Wilson Dirac operator in quenched QCD in the microscopic regime. We distinguish the topological sectors using the index as determined by the Wilson flow method. Consequently, the distributions…

High Energy Physics - Lattice · Physics 2012-01-04 Albert Deuzeman , Urs Wenger , Jair Wuilloud

A chiral random matrix model with complex eigenvalues is solved as an effective model for QCD with non-vanishing chemical potential. We derive new matrix model correlation functions which predict the local fluctuations of complex Dirac…

High Energy Physics - Theory · Physics 2009-11-07 G. Akemann

The microscopic spectral density of the Hermitian Wilson-Dirac operator is computed numerically in quenched lattice QCD. We demonstrate that the results given for fixed index of the Wilson-Dirac operator can be matched by the predictions…

High Energy Physics - Lattice · Physics 2013-05-30 P. H. Damgaard , U. M. Heller , K. Splittorff

For the massless sine-Gordon model at the free fermion point, in infinite volume, we define the fractional (charge or vertex operator) correlation functions from the probabilistic path integral and prove that they are given by renormalized…

Probability · Mathematics 2025-08-21 Roland Bauerschmidt , Scott Mason , Christian Webb

Recently, sum rules were derived for the inverse eigenvalues of the Dirac operator. They were obtained in two different ways: i) starting from the low-energy effective Lagrangian and ii) starting from a random matrix theory with the…

High Energy Physics - Theory · Physics 2016-09-06 M. A. Halasz , J. J. M. Verbaarschot