<p>The competition between bulk color superconductivity and the localized screening of a heavy quark impurity, analogous to the Kondo effect, leads to a rich spectrum of phenomena in dense quark matter. We investigate this competition at the edge of a superconducting quark bulk, where both the superconducting gap and the Kondo scale are dynamically generated in a tractable toy model. Utilizing the exact Bethe Ansatz method, we elucidate the resulting boundary physics. We identify distinct regimes characterized by either multiparticle Kondo screening or an unscreened local moment. Crucially, we also uncover a novel intermediate phase featuring impurity screening through a single-particle bound state formed within the superconducting gap. The toy model presented in this work highlights the complex interplay between dynamically generated bulk properties and boundary impurities in extreme quantum chromodynamics environments, offering potential insights into phenomena occurring in heavy-ion collisions and compact stars.</p>

United States

Pradip Kattel

Abay Zhakenov

Natan Andrei

Competing color superconductivity and color Kondo effect in quark matter

We examine the restoration of the residual gauge symmetry in the Yang–Mills theory to be regarded as a confinement criterion. For this purpose, we restrict the four-dimensional <math altimg='si14.svg'><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></math> Yang&#8211;Mills instantons to those with spatial spherical symmetry <math altimg='si15.svg'><mrow><mi>S</mi><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math>, which automatically causes the dimensional reduction of the four-dimensional <math altimg='si14.svg'><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></math> Yang&#8211;Mills theory to the two-dimensional <math altimg='si16.svg'><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math> gauge-scalar theory as implemented explicitly by the Witten transformation. In this setting, we show that the restoration of the residual gauge symmetry occurs due to condensations of instantons and anti-instantons, although the residual gauge symmetry was spontaneously broken in the perturbative vacuum. This result demonstrates that the true confinement phase is a disordered phase in which all internal electric symmetries of the gauge field remain unbroken.

Japan

Naoki Fukushima

Kei-Ichi Kondo

Residual gauge symmetry and color confinement in the Yang–Mills theory

We first study a non-relativistic field theory model for the Kondo lattice by introducing the Kondo condensation, whose main effect is the hybridization of the flat band of the localized electron with dispersive one of the itinerant electron. The problem here is that the resulting Kondo condensation arises only in strong coupling where the validity of the mean field theory is questionable. Therefore, we build a holographic mean field theory of the Kondo lattice with strong coupling by identifying the effect of the lattice with the fermion’s spectral shape due to the coupling with the order parameter representing the symmetry breaking. For the flat band spectrum we use the mixed quantization, and for the dispersive spectrum we intoduce the second fermion in standard quantization. The coupling of the two fermions with the scalar order representing the Kondo condensation provides the hybrization of the two spectrum, reproducing the main feature of the Kondo lattice together with the fuzzy character of the spectrum of the strongly coupled system.

South Korea

Young-Kwon Han

Debabrata Ghorai

Taewon Yuk

Sang-Jin Sin

Holographic mean field theory and Kondo lattice

The lattice SU(2) gauge-scalar model with the scalar field in the adjoint representation of the gauge group has two completely separated confinement and Higgs phases according to the preceding studies based on numerical simulations that have been performed in the specific gauge fixing based on the conventional understanding of the Brout-Englert-Higgs mechanism. In this paper, we reexamine this phase structure in a gauge-independent way based on the numerical simulations performed without any gauge fixing. This is motivated to confirm the recently proposed gauge-independent Brout-Englert-Higgs mechanism for generating the mass of the gauge field without relying on any spontaneous symmetry breaking. For this purpose, we investigate correlations between gauge-invariant operators obtained by combining the original adjoint scalar field and the new field called the color-direction field which is constructed from the gauge field based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi. Consequently, we reproduce gauge independently the transition line separating the confinement phase and the Higgs phase, and show surprisingly the existence of a new transition line that completely divides the confinement phase into two parts. Finally, we discuss the physical meaning of the new transition and the implications of the confinement mechanism.

Akihiro Shibata

Gauge-independent transition dividing the confinement phase in the lattice SU(2) gauge-adjoint scalar model

We consider the quantum chromodynamics (QCD) Kondo effect for a single heavy quark in quark matter composed of light quarks with chiral symmetry breaking. Introducing several spinor structures in QCD Kondo condensates, i.e., particle-projected condensate, antiparticle-projected condensate, and normal condensate without projection, we calculate the attractive energy gained by the heavy quark within the mean-field approximation in the path-integral formalism. We show that the normal condensate is favored at low density and the particle-projected condensate is favored at high density, when the light quark has a nonzero mass. We interpret such a density-dependent transition between the two condensates in terms of the Kondo resonances.

Shigehiro Yasui

Daiki Suenaga

Kei Suzuki

QCD Kondo effect for single heavy quark in chiral-symmetry broken phase

According to the preceding studies, the lattice SU(2) gauge-scalar model with a single scalar field in the fundamental representation of the gauge group has a single confinement-Higgs phase where confinement and Higgs regions are subregions of an analytically continued single phase and there are no thermodynamic phase transitions, which is a well-known consequence of the Osterwalder-Seiler-Fradkin-Shenker theorem. In this paper, we show that we can define new types of gauge-invariant operators by combining the original fundamental scalar field and the so-called color-direction field which is obtained by change of field variables based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi. By performing the numerical simulations on the lattice without any gauge fixing, we reproduce the conventional thermodynamic transition line in the weak gauge coupling, and moreover we find a new transition line detected by the new gauge-invariant operators which separates the confinement-Higgs phase into two parts, confinement phase and the Higgs phase, in the strong gauge coupling. All results are obtained in the gauge-independent way, since no gauge fixing has been imposed in the numerical simulations. Moreover, we discuss a physical interpretation for the new transition from the viewpoint of the realization of a global symmetry.

Ryu Ikeda

Seikou Kato

Gauge-independent transition separating confinement and Higgs phases in lattice SU(2) gauge theory with a scalar field in the fundamental representation

We propose a new mechanism of the heavy-quark spin polarization (HQSP) in quark matter induced by the Kondo effect under an external magnetic field. The Kondo effect is caused by a condensate between a heavy and a light quark called the Kondo condensate leading to a mixing of the heavy- and light-quark spins. Thus, the HQSP is driven through the Kondo effect from light quarks coupling with the magnetic field in quark matter. For demonstration, we employ the Nambu-Jona-Lasinio type model under a magnetic field and investigate the HQSP within the linear response theory with vertex corrections required by the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>EM</mi></mrow></msub></math> electromagnetic gauge invariance. As a result, we find that the HQSP arises significantly with the appearance of the Kondo effect. Our findings are testable in future sign-problem-free lattice simulations.

Yasufumi Araki

Heavy-quark spin polarization induced by the Kondo effect in a magnetic field

Abstract All colored particles including dynamical quarks and gluons are confined if the color confinement criterion proposed by Kugo and Ojima is satisfied. The criterion was obtained under a gauge fixing of the Lorenz type. However, it was pointed out that the Kugo–Ojima criterion breaks down for the maximal Abelian gauge, which is quite strange in view of the fact that quark confinement has been verified according to the dual superconductivity caused by magnetic monopole condensations. In order to make a bridge between Kugo–Ojima color confinement and the dual superconductor picture for quark confinement, we investigate a generalization of the color confinement criterion to obtain a unified picture for confinement. We show that the restoration of the residual local gauge symmetry which was shown in the Lorenz gauge by Hata to be equivalent to the Kugo–Ojima criterion indeed occurs in the maximal Abelian gauge for the SU(N) Yang–Mills theory in two-, three-, and four-dimensional Euclidean spacetime once the singular topological configurations of gauge fields are taken into account. This result indicates that the color confinement phase is a disordered phase caused by non-trivial topological configurations irrespective of the gauge choice. As a by-product, we show that the compact U(1) gauge theory can have a disordered confinement phase, while the non-compact U(1) gauge theory has a deconfined Coulomb phase.

Color confinement and restoration of residual local gauge symmetries

We describe the relation between integrable Kondo problems in products of chiral SU(2) WZW models and affine SU(2) Gaudin models. We propose a full ODE/IM solution of the spectral problem for these models.

Canada

Davide Gaiotto

Ji Lee

United Kingdom

Benoît Vicedo

Jingxiang Wu

Kondo line defects and affine Gaudin models

We investigate the Kondo effect with Wilson fermions. This is based on a mean-field approach for the chiral Gross-Neveu model including four-point interactions between a light Wilson fermion and a heavy fermion. For massless Wilson fermions, we demonstrate the appearance of the Kondo effect. We point out that there is a coexistence phase with both the light-fermion scalar condensate and Kondo condensate, and the critical chemical potentials of the scalar condensate are shifted by the Kondo effect. For negative-mass Wilson fermions, we find that the Kondo effect is favored near the parameter region realizing the Aoki phase. Our findings will be useful for understanding the roles of heavy impurities in Dirac semimetals, topological insulators, and lattice simulations.