scholarly journals CHIRAL SYMMETRY BREAKING AT NONZERO CHEMICAL POTENTIAL

2006 ◽  
Vol 21 (04) ◽  
pp. 859-864 ◽  
Author(s):  
J. C. Osborn ◽  
K. Splittorff ◽  
J. J. M. Verbaarschot
Keyword(s):  
Partition Function ◽  
Symmetry Breaking ◽  
Dirac Operator ◽  
Chiral Symmetry ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Chiral Condensate ◽  
Zero Temperature ◽  
Dirac Spectrum

We consider chiral symmetry breaking at nonzero chemical potential and discuss the relation with the spectrum of the Dirac operator. We solve the so called Silver Blaze Problem that the chiral condensate at zero temperature does not depend on the chemical potential while this is not the case for the Dirac spectrum and the weight of the partition function.

scholarly journals Minimally doubled fermions and spontaneous chiral symmetry breaking

2018 ◽  
Vol 175 ◽  
pp. 04002 ◽  
Author(s):  
Rudina Osmanaj (Zeqirllari) ◽  
Dafina Hyka (Xhako)
Keyword(s):  
Symmetry Breaking ◽  
Dirac Operator ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Chiral Condensate ◽  
Low Energy ◽  
Reliable Determination ◽  
Spontaneous Chiral Symmetry Breaking ◽  
Energy Physics

Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks – Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss – Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.

MESONS AND DIQUARKS IN A NJL MODEL AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL

1993 ◽  
Vol 08 (07) ◽  
pp. 1295-1312 ◽  
Author(s):  
D. EBERT ◽  
YU. L. KALINOVSKY ◽  
L. MÜNCHOW ◽  
M.K. VOLKOV
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Baryon Number ◽  
Coupling Constants ◽  
Number Density ◽  
Njl Model

An extended NJL model with [Formula: see text] and (qq)-interactions is studied at finite temperature and baryon number density. We investigate the chiral symmetry breaking, its restoration and the behavior of meson and diquark masses, decay and coupling constants as functions of T and µ.

scholarly journals Chiral symmetry breaking by monopole condensation

2017 ◽  
Vol 32 (23n24) ◽  
pp. 1750139 ◽  
Author(s):  
Aiichi Iwazaki
Keyword(s):  
Symmetry Breaking ◽  
Pair Production ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Chiral Condensate ◽  
Low Energy ◽  
Chiral Anomaly ◽  
Symmetric Pair ◽  
Color Charge ◽  
Massless Quark

Under the assumption of Abelian dominance in QCD, we have shown that chiral condensate is locally present around each QCD monopole. The essence is that either charge or chirality of a quark is not conserved, when the low energy massless quark collides with QCD monopole. In reality, the charge is conserved so that the chirality is not conserved. Reviewing the presence of the local chiral condensate, we show by using chiral anomaly that chiral nonsymmetric quark pair production takes place when a color charge is putted in a vacuum with monopole condensation, while chiral symmetric pair production takes place in a vacuum with no monopole condensation. Our results strongly indicate that the chiral symmetry is broken by the monopole condensation.

NEARLY CONFORMAL GAUGE THEORIES ON THE LATTICE

2010 ◽  
Vol 25 (27n28) ◽  
pp. 5162-5174 ◽  
Author(s):  
ZOLTÁN FODOR ◽  
KIERAN HOLLAND ◽  
JULIUS KUTI ◽  
DÁNIEL NÓGRÁDI ◽  
CHRIS SCHROEDER
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Gauge Theories ◽  
Matrix Theory ◽  
Chiral Symmetry Breaking ◽  
Chiral Condensate ◽  
Theoretical Understanding ◽  
Conformal Window ◽  
Running Coupling ◽  
Conformal Gauge

We present selected new results on chiral symmetry breaking in nearly conformal gauge theories with fermions in the fundamental representation of the SU (3) color gauge group. We found chiral symmetry breaking (χSB) for all flavors between Nf = 4 and Nf = 12 with most of the results discussed here for Nf = 4, 8, 12 as we approach the conformal window. To identify χSB we apply several methods which include, within the framework of chiral perturbation theory, the analysis of the Goldstone spectrum in the p -regime and the spectrum of the fermion Dirac operator with eigenvalue distributions of random matrix theory in the ϵ-regime. Chiral condensate enhancement is observed with increasing Nf when the electroweak symmetry breaking scale F is held fixed in technicolor language. Important finite-volume consistency checks from the theoretical understanding of the SU(Nf) rotator spectrum of the δ-regime are discussed. We also consider these gauge theories at Nf = 16 inside the conformal window. Our work on the running coupling is presented separately.1

STANDING WAVE GROUND STATE IN HIGH DENSITY, ZERO TEMPERATURE QCD AT LARGE NC

1992 ◽  
Vol 07 (04) ◽  
pp. 659-681 ◽  
Author(s):  
D. V. DERYAGIN ◽  
D. YU. GRIGORIEV ◽  
V. A. RUBAKOV
Keyword(s):  
Symmetry Breaking ◽  
Standing Wave ◽  
Ground State ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Mass Operator ◽  
Ladder Approximation ◽  
Zero Temperature ◽  
Density Zero ◽  
Bilocal Field

Chiral symmetry breaking in QCD at zero temperature and high fermionic density is studied in the limit NC → ∞. We evaluate the effective action in the ladder approximation and integrate out fermions by introducing the bilocal field Σ(x, y), which enters the action as the mass operator for fermions. It is argued that at large fermionic chemical potential the mass operator Σ(x, y) has a small but nonvanishing expectation value. The condensate of the field Σ(x, y) and the fermionic condensate [Formula: see text] are inhomogeneous and anisotropic, so that the ground state has the structure of the standing wave with respect to these order parameters. Unlike possible color superconductivity, this symmetry breaking occurs to the leading order in 1/NC.

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