scholarly journals Monopole and instanton effects in QCD

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Masayasu Hasegawa
Keyword(s):  
Dirac Operator ◽  
Matrix Theory ◽  
Charged Pion ◽  
Lattice Gauge Theory ◽  
Pion Mass ◽  
Magnetic Monopoles ◽  
Chiral Condensate ◽  
Creation Operator ◽  
Experimental Result ◽  
Qcd Vacuum

Abstract We aim to show the effects of the magnetic monopoles and instantons in quantum chromodynamics (QCD) on observables; therefore, we introduce a monopole and anti-monopole pair in the QCD vacuum of a quenched SU(3) by applying the monopole creation operator to the vacuum. We calculate the eigenvalues and eigenvectors of the overlap Dirac operator that preserves the exact chiral symmetry in lattice gauge theory using these QCD vacua. We then investigate the effects of magnetic monopoles and instantons. First, we confirm the monopole effects as follows: (i) the monopole creation operator makes the monopoles and anti-monopoles in the QCD vacuum. (ii) A monopole and anti-monopole pair creates an instanton or anti-instanton without changing the structure of the QCD vacuum. (iii) The monopole and anti-monopole pairs change only the scale of the spectrum distribution without affecting the spectra of the Dirac operator by comparing the spectra with random matrix theory. Next, we find the instanton effects by increasing the number density of the instantons and anti-instantons as follows: (iv) the decay constants of the pseudoscalar increase. (v) The values of the chiral condensate, which are defined as negative numbers, decrease. (vi) The light quarks and the pseudoscalar mesons become heavy. The catalytic effect on the charged pion is estimated using the numerical results of the pion decay constant and the pion mass. (vii) The decay width of the charged pion becomes wider than the experimental result, and the lifetime of the charged pion becomes shorter than the experimental result. These are the effects of the monopoles and instantons in QCD.

scholarly journals Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
G. Akemann ◽  
T. R. Würfel
Keyword(s):  
Dirac Operator ◽  
Random Matrix ◽  
Correlation Functions ◽  
Matrix Theory ◽  
Chiral Condensate ◽  
Effect Of Temperature ◽  
Specific Class ◽  
Chiral Phase ◽  
Determinantal Representation ◽  
Matrix Ensemble

Abstract In the ε-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 matrix ensemble has been proposed, where a constant, deterministic matrix is added to the Dirac operator. Its eigenvalue correlation functions can be written as the determinant of a kernel that depends on temperature. Due to recent progress in this specific class of random matrix ensembles, featuring a deterministic, additive shift, we can determine the limiting kernel and correlation functions in this class, which is the class of polynomial ensembles. We prove the equivalence between this new determinantal representation of the microscopic eigenvalue correlation functions and existing results in terms of determinants of different sizes, for an arbitrary number of quark flavours, with and without temperature, and extend them to non-zero topology. These results all agree and are thus universal when measured in units of the temperature dependent chiral condensate, as long as we stay below the chiral phase transition.

scholarly journals Updates on the QCD phase diagram from lattice

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Sayantan Sharma
Keyword(s):  
Phase Diagram ◽  
Lattice Gauge Theory ◽  
Topological Properties ◽  
Chiral Phase ◽  
Qcd Phase Diagram ◽  
Qcd Vacuum ◽  
Lattice Gauge ◽  
Massless Quark ◽  
Quark Flavors

AbstractDifferent aspects of the phase diagram of strongly interacting matter described by quantum chromodynamics (QCD), which have emerged from the recent studies using lattice gauge theory techniques, are discussed. A special emphasis is given on understanding the role of the anomalous axial U(1) symmetry in determining the order of the finite temperature chiral phase transition in QCD with two massless quark flavors and tracing its origin to the topological properties of the QCD vacuum.

scholarly journals Chiral condensate and Dirac spectrum of one-and two-flavor QCD at nonzero θ-angle

2018 ◽  
Vol 175 ◽  
pp. 04004 ◽  
Author(s):  
Mario Kieburg ◽  
Jacobus Verbaarschot ◽  
Tilo Wettig
Keyword(s):  
Dirac Operator ◽  
Quark Mass ◽  
Imaginary Axis ◽  
Chiral Condensate ◽  
Dirac Spectrum ◽  
Quark Masses ◽  
Zero Modes

In previous work we showed that the chiral condensate of one-flavor QCD exhibits a Silver Blaze phenomenon when the quark mass crosses m = 0: the chiral condensate remains constant while the quark mass crosses the spectrum of the Dirac operator, which is dense on the imaginary axis. This behavior can be explained in terms of exponentially large cancellations between contributions from the zero modes and from the nonzero modes when the quark mass is negative. In these proceedings we show that a similar Silver Blaze phenomenon takes places for QCD with one flavor and arbitrary θ- angle, and for QCD with two flavors with different quark masses m1 and m2. In the latter case the chiral condensate remains constant when m1 crosses zero at fixed m2 > 0 until the Dashen point m1 = –m2 is reached, where the chiral condensate has a discontinuity. In terms of contributions from the Dirac spectrum the shift of the discontinuity from m1 = 0 to m1 = -m2 also arises from exponentially large cancellations between the zero and nonzero modes when m1m2 < 0. All calculations are performed in the microscopic or ε-domain of QCD. Results for arbitrary θ-angle are discussed as well.

Quantum chromodynamics

2018 ◽  
Author(s):  
Marcos Marino
Keyword(s):  
Symmetry Breaking ◽  
Dirac Operator ◽  
Global Symmetries ◽  
Quantum Chromodynamics ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Matrix Theory ◽  
Global Symmetry

This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.

scholarly journals Magnetic monopoles and the dual London equation in SU(3) lattice gauge theory

1997 ◽  
Vol 53 (1-3) ◽  
pp. 518-520
Author(s):  
Peter Skala ◽  
Manfried Faber ◽  
Martin Zach
Keyword(s):  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Magnetic Monopoles ◽  
Lattice Gauge ◽  
London Equation

Charged Pion Mass Determination and Energy — Calibration Standards Based on Pionic X-ray Transitions

2001 ◽  
pp. 500-507
Author(s):  
D. F. Anagnostopoulos ◽  
M. Augsburger ◽  
G. Borchert ◽  
D. Chatellard ◽  
P. El-Khoury ◽  
...  
Keyword(s):  
Charged Pion ◽  
Pion Mass ◽  
Energy Calibration ◽  
Mass Determination ◽  
Calibration Standards ◽  
X Ray

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

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.

Sign in / Sign up

Export Citation Format

Share Document