We develop a manifestly gauge-covariant expansion and projection using the eigen-mode of the QCD Dirac operator. Applying this method to the Wilson loop and the Polyakov loop, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in SU(3) lattice QCD calculation on 6^4 at beta=5.6 at the quenched level. Notably, the Wilson loop is found to obey the area law, and the slope parameter corresponding to the string tension or the confinement force is almost unchanged, even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking. We find also that the Polyakov loop remains to be almost zero even without the low-lying Dirac modes, which indicates the Z_3-unbroken confinement phase. These results indicate that one-to-one correspondence does not hold between confinement and chiral symmetry breaking in QCD.
We represent Polyakov loops and their correlators as spectral sums of eigenvalues and eigenmodes of the lattice Dirac operator. The deconfinement transition of pure gauge theory is characterized as a change in the response of moments of eigenvalues to varying the boundary conditions of the Dirac operator. We argue that the potential between static quarks is linked to spatial correlations of Dirac eigenvectors.
Using the eigen-mode of the QCD Dirac operator $\Slash D=γ^μD^μ$, we develop a manifestly gauge-covariant expansion and projection of the QCD operators such as the Wilson loop and the Polyakov loop. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD Monte Carlo calculations. Even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking, we find that the Wilson loop obeys the area law, and the string tension or the confinement force is almost unchanged. We find also that the Polyako…
Using the eigen-mode of the QCD Dirac operator $\Slash D=γ^μD^μ$, we develop a manifestly gauge-covariant expansion and projection of the QCD operators such as the Wilson loop and the Polyakov loop. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD Monte Carlo calculation on $6^4$ at $β$=5.6. Even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking, we find that the Wilson loop obeys the area law, and the slope parameter corresponding to the string tension or the confinement …
We analytically study the relation between quark confinement and spontaneous chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive some formulae for the Polyakov loop, its fluctuations, and the string tension from the Wilson loop. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain wall fermion kernels, respectively. For the confinement quantities, the low-lying Dirac/fermion eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. These relations indicate no direct …
We compute complete spectra of the staggered lattice Dirac operator for quenched SU(3) gauge configurations below and above the critical temperature. The confined and the deconfined phase are characterized by a different response of the Dirac eigenvalues to a change of the fermionic boundary conditions. We analyze the role of the eigenvalues in recently developed spectral sums representing the Polyakov loop. We show that the Polyakov loop gets its main contributions from the UV end of the spectrum.
Chiral dynamics is investigated using the chiral confining Lagrangian (CCL), previously derived from QCD with confinement interaction. Based on the calculations of the quark condensate, which is defined entirely by confinement in the zero quark mass limit, one can assert that chiral symmetry breaking occurs not spontaneously but is predetermined by confinement. The expansion of the CCL provides the GMOR relations and the effective chiral Lagrangian, which is used to provide the masses and decay constants of all chiral mesons, including $η,η'$. For the latter one needs to define a non-chiral co…
We construct an effective Lagrangian which illustrates why color deconfines when chiral symmetry is restored in hot gauge theories with quarks in the fundamental representation. For quarks in the adjoint representation we show that while deconfinement and the chiral transition do not need to coincide, entanglement between them is still present. Extension to the chemical potential driven transition is discussed.
We investigate the relevant gluon-momentum region for confinement in lattice QCD on $16^4$ at $β$=5.7, 5.8 and 6.0, based on the Fourier expansion. We find that the string tension $σ$, i.e., the confining force, is almost unchanged even after removing the high-momentum gluon component above 1.5GeV in the Landau gauge. In fact, the confinement property originates from the low-momentum gluon component below 1.5GeV, which is the upper limit to contribute to $σ$. In the relevant region, smaller gluon momentum component is more important for confinement. Next, we develop a manifestly gauge-covarian…
In this paper we study the properties of QCD at nonzero chiral density $ρ_5$, which is introduced through chiral chemical potential $μ_5$. The study is performed within lattice simulation of QCD with dynamical rooted staggered fermions. We first check that $ρ_5$ is generated at nonzero $μ_5$ and in the chiral limit observe $ρ_5 \sim Λ_{QCD}^2 μ_5$. We also test the possible connection between confinement and topological fluctuations. To this end, we measured the topological susceptibility $χ_{\mbox{\footnotesize top}}$ and string tension $σ$ for various values of $μ_5$. We observed that both s…
Confinement without symmetry breaking in chiral gauge theories
School of Physics, Sun Yat-Sen University（中山大学物理学院）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学中心（iTHEMS））；Centre for Cosmology, Particle Physics and Phenomenology (CP3), Université catholique de Louvain（天主教鲁汶大学宇宙学、粒子物理与现象学中心（CP3））
We analyze the vacuum structure of SU(2) QCD with multiple massless adjoint representation fermions formulated on a small spatial $S^1 \times \R^3$. The absence of thermal fluctuations, and the fact that quantum fluctuations favoring the vacuum with unbroken center symmetry in a weakly coupled regime renders the interesting dynamics of these theories analytically calculable. Confinement, the area law behavior for large Wilson loops, and the generation of the mass gap in the gluonic sector are shown analytically. By abelian duality transformation, the long distance effective theory of QCD is ma…
Two-dimensional QED with $N$ flavor fermions is solved at zero and finite temperature with arbitrary fermion masses to explore QCD physics such as chiral condensate and string tension. The problem is reduced to solving a Schrödinger equation for $N$ degrees of freedom with a specific potential determined by the ground state of the Schrödinger problem itself.
In lattice QCD formalism, we derive an analytical gauge-invariant relation between the Polyakov loop $\langle L_P \rangle$ and the Dirac eigenvalues $λ_n$ in QCD, i.e., $\langle L_P \rangle \propto \sum_n λ_n^{N_t -1} \langle n|\hat U_4|n \rangle$, by considering ${\rm Tr} (\hat{U}_4\hat{\not{D}}^{N_t-1})$ on a temporally odd-number lattice, where the temporal lattice size $N_t$ is odd. This formula is a Dirac spectral representation of the Polyakov loop in terms of Dirac eigenmodes $|n\rangle$. We here use an ordinary square lattice with the normal (nontwisted) periodic boundary condition for…
We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various "confinement indicators", such as the Polyakov loop, its fluctuations, the Wilson loop, the inter-quark potential and the string tension, in terms of the Dirac eigenmodes. In the Dirac spectral representation, there appears a power of the Dirac eigenvalue $λ_n$ such as $λ_n^{N_t-1}$, which behaves as a reduction factor for small $λ_n$. Consequently, since this reduction factor cannot be cancelled, the low-lying Dirac eigenmodes give negligibly sm…
In the lattice QCD formalism, we derive a gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes on a temporally odd-number lattice, where the temporal lattice size is odd, with the normal (nontwisted) periodic boundary condition. This analytical relation indicates that low-lying Dirac modes have little contribution to the Polyakov loop. Using lattice QCD simulations, we numerically confirm the analytical relation and the negligible contribution of low-lying Dirac modes to the Polyakov loop at the quenched level, i.e., the Polyakov loop is almost unchanged by remo…
To clarify the relation between confinement and chiral symmetry breaking in QCD, we consider a temporally odd-number lattice, with the temporal lattice size $N_t$ being odd. We here use an ordinary square lattice with the normal (nontwisted) periodic boundary condition for link-variables in the temporal direction. By considering ${\rm Tr} (\hat{U}_4\hat{\not D}^{N_t-1})$, we analytically derive a gauge-invariant relation between the Polyakov loop $\langle L_P \rangle$ and the Dirac eigenvalues $λ_n$ in QCD, i.e., $\langle L_P \rangle \propto \sum_n λ_n^{N_t -1} \langle n|\hat U_4|n \rangle$, w…
We investigate the contribution from each Dirac modes to the Polyakov loop based on a gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes on a temporally odd-number lattice, where the temporal lattice size is odd, with the normal (nontwisted) periodic boundary condition. The dumping factor in the relation plays crucial role for the negligible contribution of low-lying Dirac modes to the Polyakov loop. The zero-value of the Polyakov loop in the confinement phase is due to the ``positive/negative symmetry'' of the Dirac-mode contribution to the Polyakov loop. In …
We study the relation between quark confinement and spontaneous chiral-symmetry breaking directly in QCD. In lattice QCD formalism, we derive an analytical gauge-invariant relation between the Polyakov loop $\langle L_P \rangle$ and the Dirac eigenvalues $λ_n$, i.e., $\langle L_P \rangle \propto \sum_n λ_n^{N_t -1} \langle n|\hat U_4|n \rangle$, on a temporally odd-number lattice, where the temporal lattice size $N_t$ is odd. Here, $|n \rangle$ denotes the Dirac eigenmode, i.e., $\not D|n \rangle=iλ_n|n \rangle$, and $\hat U_4$ the temporal link-variable operator. We here use an ordinary squar…
Employing functional approaches the infrared behaviour of Landau gauge QCD vertex functions is investigated. Results for the ghost-gluon, three-gluon and quark-gluon vertex functions are presented. As can be analytically shown a linear rising potential between heavy quarks is generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities implies the existence of scalar Dirac amplitudes of the full vertex and the quark propagator. These amplitudes can only be present when chiral symmetry is broken, either explicitly or dyna…
Inspired by the construction of the Gribov-Zwanziger action in the Landau gauge, we introduce a quark model exhibiting both confinement and chiral symmetry aspects. An important feature is the incorporation of spontaneous chiral symmetry breaking in a renormalizable fashion. The quark propagator in the condensed vacuum turns out to be of a confining type. Besides a real pole, it exhibits complex conjugate poles. The resulting spectral form is explicitly shown to violate positivity, indicative of its unphysical character. Moreover, the ensuing quark mass function fits well to existing lattice d…
Two crucial properties of QCD, confinement and chiral symmetry breaking, cannot be understood within the context of conventional Feynman perturbation theory. Non-perturbative phenomena enter the theory in a fundamental way at both the classical and quantum level. Over the years a coherent qualitative picture of the interplay between chiral symmetry, quantum mechanical anomalies, and the lattice has emerged and is reviewed here.
Ample numerical evidence from lattice calculations shows a strong connection between the confining properties of gauge theories at finite temperature and the localisation properties of the low-lying Dirac eigenmodes. In this contribution we discuss recent progress on this topic, focussing on results for QCD at imaginary chemical potential $μ_I/T = π$ at temperatures above the Roberge-Weiss transition temperature. These confirm the general picture of low modes turning from delocalised to localised at the deconfinement transition, in a previously unexplored setup with a genuine, physical transit…
The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chir…
We study the QCD phase diagram, in particular we study the critical points of the two main QCD phase transitions, confinement and chiral symmetry breaking. Confinement drives chiral symmetry breaking, and, due to the finite quark mass, at small density both transitions are a crossover, while they are a first or second order phase transition in large density. We study the QCD phase diagram with a quark potential model including both confinement and chiral symmetry. This formalism, in the Coulomb gauge hamiltonian formalism of QCD, is presently the only one able to microscopically include both a…
We review arguments that chiral symmetry breaking is triggered when the quark bilinear condensate's dimension passes through one ($γ=1$). This is supported by gap equations and more recently holographic models. Confinement may then be a separate property of the pure Yang-Mills theory below the scale of the dynamically generated quark mass, occurring at the scale of the pole in the deep IR running. Here, we use perturbative results for the running of the gauge coupling and $γ$ in asymptotically free SU($N_c$) gauge theories with matter in higher dimension representations to seek the best candid…
The chirally symmetric overlap quark propagator is explored in Coulomb gauge for the first time. This gauge is especially well suited for studying the interrelation between confinement and chiral symmetry breaking, since confinement can be attributed to the infrared divergence of the vector dressing function of the inverse quark propagator. Using quenched gauge field configurations on a $20^4$ lattice, the dressing functions of the quark propagator as well as the dynamical quark mass function are evaluated, also in the chiral limit. Chiral symmetry is artificially restored by removing the low …
We use lattice QCD simulations to test some of the predictions of proposed AdS/QCD (holographic) duals for QCD. In particular, these duals predict that the scale of chiral symmetry breaking ($χ$SB) can be varied independently from that of confinement, with the proviso that the scale of $χ$SB cannot be longer than that of confinement. We simulate lattice QCD with 2 quarks in the fundamental representation of colour and with additional 4-fermion interactions (suggested by AdS/QCD), at finite temperatures. For sufficiently strong 4-fermion interactions, the deconfinement and $χ$SB transitions occ…
We study the QCD phase diagram, in particular we study the critical points of the two main QCD phase transitions, confinement and chiral symmetry breaking. Confinement drives chiral symmetry breaking, and, due to the finite quark mass, at small density both transitions are a crossover, while they are a first or second order phase transition in large density. We study the QCD phase diagram with a quark potential model including both confinement and chiral symmetry. This formalism, in the Coulomb gauge hamiltonian formalism of QCD, is presently the only one able to microscopically include both a…
A key question to QCD is what mechanism generates the hadron mass in the light quark sector, where both confinement and chiral symmetry breaking are in the game. Are confinement and chiral symmetry breaking in the vacuum uniquely interconnected? Can hadrons survive chiral symmetry restoration? If yes, what happens with their mass and what symmetries beyond the chiral symmetry are there? We review our recent insights. In particular, in a dynamical lattice simulation we artificially restore chiral symmetry by removing the low-lying Dirac modes of the valence quark propagators, which is a well de…
We study interplay between confinement/deconfinement and chiral properties. We derive some analytical relations of the Dirac modes with the confinement quantities, such as the Polyakov loop, its susceptibility and the string tension. For the confinement quantities, the low-lying Dirac eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. This indicates no direct, one-to-one correspondence between confinement/deconfinement and chiral properties in QCD. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clove…
Suggested holographic duals of QCD, based on AdS/CFT duality, predict that one should be able to vary the scales of colour confinement and chiral-symmetry breaking independently. Furthermore they suggest that such independent variation of scales can be achieved by the inclusion of extra 4-fermion interactions in QCD. We simulate lattice QCD with such extra 4-fermion terms at finite temperatures and show that for strong enough 4-fermion couplings the deconfinement transition occurs at a lower temperature than the chiral-symmetry restoration transition. Moreover the separation of these transitio…
We investigate which momentum components of gluons induce color confinement and spontaneous chiral symmetry breaking in lattice QCD. For this purpose, we formulate a lattice framework to introduce the momentum cutoff of the gluon field. Using this framework, we calculate the quark-antiquark potential, the color flux tube, the chiral condensate, and the Dirac spectrum. Our results suggest that confinement and chiral symmetry breaking are induced by somehow different momentum components of gluons.
We study the gravitational-wave signal stemming from strongly coupled models featuring both, dark chiral and confinement phase transitions. We therefore identify strongly coupled theories that can feature a first-order phase transition. Employing the Polyakov-Nambu-Jona-Lasinio model, we focus our attention on SU(3) Yang-Mills theories featuring fermions in fundamental, adjoint, and two-index symmetric representations. We discover that for the gravitational-wave signals analysis, there are significant differences between the various representations. Interestingly we also observe that the two-i…
The mass function of the nonperturbative quark propagator in SU(3) gauge theory shows only a weak dependence on the vortex content of the gauge configurations. Of particular note is the survival of dynamical mass generation on vortex-free configurations having a vanishing string tension. This admits the possibility that mass generation associated with dynamical chiral symmetry breaking persists without confinement. In this presentation, we examine the low-lying ground-state hadron spectrum of the pi, rho, N and Delta and discover that while dynamical mass generation persists in the vortex-free…
The gap equation is a cornerstone in understanding dynamical chiral symmetry breaking and may also provide clues to confinement. A symmetry-preserving truncation of its kernel enables proofs of important results and the development of an efficacious phenomenology. We describe a model of the kernel that yields: a momentum-dependent dressed-quark propagator in fair agreement with quenched lattice-QCD results; and chiral limit values: f_pi= 68 MeV and <q-bar q> = -(190 MeV)^3. It is compared with models inferred from studies of the gauge sector.
Continuum strong QCD is the application of models and continuum quantum field theory to the study of phenomena in hadronic physics, which includes; e.g., the spectrum of QCD bound states and their interactions. Herein I provide a Dyson-Schwinger equation perspective, focusing on qualitative aspects of confinement and dynamical chiral symmetry breaking in cold, sparse QCD, and also elucidating consequences of the axial-vector Ward-Takahashi identity and features of the heavy-quark limit.
We investigate the quark number density at finite imaginary chemical potential by using the Dirac-mode expansion. In the large quark mass region, it is found that the quark number density can be expressed by the Polyakov loop and its conjugate in all order of the large quark mass expansion. Then, there are no specific Dirac-modes which dominantly contribute to the quark number density. In comparison, the small quark mass region is explored by using the quenched lattice QCD simulation. We found that the absolute value of the quark number density strongly depends on the low-lying Dirac-modes, bu…
The chiral Jacobian, which is defined with Neuberger's overlap Dirac operator of the lattice fermion, is explicitly evaluated in the continuum limit without expanding it in the gauge coupling constant. Our calculational scheme is simple and straightforward. We determine a coefficient of the chiral anomaly for general values of the mass parameter and the Wilson parameter of the overlap Dirac operator.
The chiral Dirac determinant is calculated using the overlap formalism of Narayanan and Neuberger. We compare the real and imaginary parts of the determinant with the continuum result for perturbative gauge field backgrounds and show that they are identical. Thus we find that the overlap formalism passes a crucial test.
As a color confinement mechanism, a dual Meissner effect due to Abelian monopoles involved in QCD has been discussed so far in various ways. But still there is an important problem unsolved. It is gauge invariance of the schemes or, in other words, the reason why non-Abelian color confinement is explained by means of the Abelian dual Meissner effect. Here it is shown that a random Abelian method based on the violation of non-Abelian Bianchi identity (VNABI) could prove SU(3) invariance and explain why color-singlets alone can survive in the confinement phase of QCD in the framework of the Abel…
The review of vacuum and matter restructuring in space-time with boundaries is presented. We consider phase properties of confining gauge theories and strongly interacting fermion systems. In particular, the chiral and deconfinement phase transitions properties in the presence of Casimir plates. We also discuss mass scale shifts in such systems and their possible dynamical and geometrical nature.
We apply to lattice QCD a bosonization method previously developed in which dynamical bosons are generated by time-dependent Bogoliubov transformations. The transformed action can be studied by an expansion in the inverse of the nilpotency index, which is the number of fermionic states in the structure function of composite bosons. When this number diverges the model is solved by the saddle point method which has a variational interpretation. We give a stationary covariant solution for a background matter field whose fluctuations describe mesons. In the saddle point approximations live fermion…
I discuss recent results on the relation between the localisation of low-lying Dirac eigenmodes, the restoration of chiral symmetry, and deconfinement in QCD and QCD-like models, providing evidence of a close connection between the three phenomena.
We discuss theories with the exceptional centerless gauge group G(2), paying attention to confinement and the pattern of chiral symmetry breaking. Exploiting the Higgs mechanism to break the symmetry down to SU(3), we also present how the familiar features of confinement and chiral symmetry breaking of SU(3) gauge theories reemerge. G(2) gauge theories show up as an unusual theoretical framework to study SU(3) gauge theories without the ``luxury'' of a center.
Adopting the cooling technique to smooth the discontinuous Z(2) lattice gauge field, we found that on SU(2) gauge configurations obtained by this smoothing there exists clear discontinuity of the topological property at almost the same point as the confinement-deconfinement phase transition of the original Z(2) gauge theory. This observation suggests the possibility that Z(2) gauge model might be a testbed for analyzing the relation between the confinement and the chiral phase transition in which the topological objects are believed to play crucial roles.
We study the QCD phase diagram, in particular we study the critical points of the two main QCD phase transitions, confinement and chiral symmetry breaking. Confinement drives chiral symmetry breaking, and, due to the finite quark mass, at small density both transitions are a crossover, while they are a first or second order phase transition in large density. We study the QCD phase diagram with a quark potential model including both confinement and chiral symmetry. We present the confinement of quark fields into a flux tube, obtained in SU(3) quenched lattice QCD, to illustrate the importance o…
Using the Dirac-mode expansion method, which keeps the gauge invariance, we analyze the Polyakov loop in terms of the Dirac modes in SU(3) quenched lattice QCD in both confined and deconfined phases. First, to investigate the direct correspondence between confinement and chiral symmetry breaking, we remove low-lying Dirac-modes from the confined vacuum generated by lattice QCD. In this system without low-lying Dirac modes, while the chiral condensate $\langle \bar{q} q\rangle$ is extremely reduced, we find that the Polyakov loop is almost zero and $Z_3$-center symmetry is unbroken, which indic…
In the lattice QCD formalism, we investigate the relation between confinement and chiral symmetry breaking. A gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes is derived on a temporally odd-number lattice, where the temporal lattice size is odd, with the normal (nontwisted) periodic boundary condition for link-variables. This analytical relation indicates that low-lying Dirac modes have little contribution to the Polyakov loop, and it is numerically confirmed at the quenched level in both confinement and deconfinement phases. This fact indicates no direct on…
We establish that QED3 can possess a critical number of flavours, N_f^c, associated with dynamical chiral symmetry breaking if, and only if, the fermion wave function renormalisation and photon vacuum polarisation are homogeneous functions at infrared momenta when the fermion mass function vanishes. The Ward identity entails that the fermion-photon vertex possesses the same property and ensures a simple relationship between the homogeneity degrees of each of these functions. Simple models for the photon vacuum polarisation and fermion-photon vertex are used to illustrate these observations. Th…
We report on a mean-field study of spontaneous breaking of chiral symmetry for Dirac fermions with contact interactions in the presence of chiral imbalance, which is modelled by nonzero chiral chemical potential. We point out that chiral imbalance lowers the vacuum energy of Dirac fermions, which leads to the increase of the renormalized chiral chemical potential upon chiral symmetry breaking. The critical coupling strength for the transition to the broken phase is slightly lowered as the chiral chemical potential is increased, and the transition itself becomes milder. Furthermore, we study th…
In this preliminary study, we examine the chiral properties of the parametrized Fixed-Point Dirac operator D^FP, see how to improve its chirality via the Overlap construction, measure the renormalized quark condensate Sigma and the topological susceptibility chi_t, and investigate local chirality of near zero modes of the Dirac operator. We also give a general construction of chiral currents and densities for chiral lattice actions.
The Polyakov loop and the Dirac modes are connected via a simple analytical relation on the temporally odd-number lattice, where the temporal lattice size is odd with the normal (nontwisted) periodic boundary condition. Using this relation, we investigate the relation between quark confinement and chiral symmetry breaking in QCD. In this paper, we discuss the properties of this analytical relation and numerically investigate each Dirac-mode contribution to the Polyakov loop in both confinement and deconfinement phases at the quenched level. This relation indicates that low-lying Dirac modes ha…
Interesting lattice QCD simulations at high temperature in QCD and particular truncated studies have shown the emergence of an unexpected group symmetry, so called \textit{chiralspin}. However this is not a symmetry of the QCD action for free quarks, which makes unclear the transition to deconfinement at high temperature in QCD. Therefore we try to redefine this group so that is a symmetry of free quark action and it is consistent with the presence of deconfinement in QCD.
We present results of $SU(3)$ Monte-Carlo studies of a new color confinement scheme due to Abelian-like monopoles of the Dirac type without any gauge-fixing. We get (1) perfect Abelian dominance with respect to the static potentials on $12^4\sim 16^4$ lattice at $β=5.6-5.8$ using the multilevel method, (2) monopole as well as Abelian dominances with respect to the static potentials by evaluating Polyakov loop correlators on $24^3\times4$ lattice at $β=5.6$. (3) Abelian dual Meissner effects are studied directly by measuring Abelian color fields and monopole currents around the static source. T…
We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral Random Matrix Theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral Perturbation Theory. All results are obtained for fixed index of th…
In this paper we study how dynamical chiral symmetry breaking is affected by nonzero chiral chemical potential in Dirac semimetals. To perform this study we applied lattice quantum Monte Carlo simulations of Dirac semimetals. Within lattice simulation we calculated the chiral condensate for various fermion masses, the chiral chemical potentials and effective coupling constants. For all parameters under consideration we have found that the chiral condensate is enhanced by chiral chemical potential. Thus our results confirms that in Dirac semimetals the chiral chemical potential plays a role of …
