nteractions in the hot and dense QCD medium give rise to extensive mixing between hadronic and gluonic degrees of freedom. The resulting mass matrix is non-Hermitian, which can lead to moat regimes with spatial modulations and instabilities towards inhomogeneous phases. I will discuss the underlying physics, implications for the QCD phase diagram and experimental opportunities.

In this talk, I will report our recent achievements based on refs. [1,2]. Below are highlights from our results.

**Perturbative Confinement under Imaginary Rotation**

We perturbatively calculated the Polyakov loop potential at high $T$ with *imaginary* angular velocity. Under the rapid imaginary rotation, the potential favors zero Polyakov loop, i.e. confinement. In ref. [1], we found a...

The core goal of heavy-ion collision experiments is to shed light on how the phases and properties of strong-interaction matter arise from the fundamental constituents and interactions of QCD. But even if macroscopic critical behaviors are finally established in experiments, how do they arise from the microscopic degrees of freedom, the quarks and gluons, remains to be solved. In this talk we...

We present an update on the study of the finite temperature QCD phase transition at zero baryon chemical potential with 3 degenerate flavors of Mobius domain wall fermions. The simulation is performed on lattice extent $N_t=12$ with lattice spacing $a=0.1361(20)$ fm, corresponding to temperature around 121(2) MeV.

We investigate a range of quark masses and two different volumes with aspect...

In this presentation, we explore the phase diagram of (2+1)-flavor Quantum Chromodynamics (QCD) through the study of fluctuations of conserved charges using Domain Wall Fermions (DWF). DWF are known for their better control over chiral symmetry, closely matching the symmetries of continuum QCD. This implies that studies of QCD phase transitions using DWF fall within the same universality class...

The Schwinger-Keldysh functional renormalization group (fRG) is employed to investigate critical dynamics of Model A and Model H that is related to second-order phase transition in the QCD phase diagram. The purely dissipative relaxation of a non-conserved field is described in Model A. The effective action of model A is expanded to the order of $O(\partial^2)$ in the derivative expansion for...

We present the first non-perturbative determination of the magnetic field dependence of the QCD topological susceptibility for temperatures in the crossover region from Lattice QCD. At low temperatures we observe that the sum rule that relates the magnetic field dependence of the susceptibility and the chiral condensate is maintained well beyond the weak magnetic field limit. Furthermore we...

We present the first lattice QCD results of quadratic fluctuations and correlations of conserved charges in (2+1)-flavor lattice QCD in the presence of a background magnetic field. The simulations were performed using the Highly Improved Staggered Quarks with physical pion mass $m_\pi$ = 135 MeV on $N_\tau=8$ and 12 lattices. We find that the correlation between net baryon number and electric...

We study the nature of charm degrees of freedom in hot strong interaction matter by performing lattice QCD calculations of the second and fourth-order cumulants of charm fluctuations, and their correlations with net baryon number, electric charge and strangeness fluctuations. We show that below the chiral crossover temperature, the thermodynamics of charm can be very well understood in terms...

We discuss the QCD phase diagram in strong magnetic fields, where the chiral condensate is enhanced by the magnetic catalysis mechanism. In contrast to the conventional discussions, we include heavy-quark impurities that have been known to induce the Kondo effect. We propose a quantum critical point that arises as a consequence of the Kondo effect and the chiral symmetry breaking. Our phase...

We study one-flavor $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ lattice QCD in ($1+1$) dimensions at zero temperature and finite density using matrix product states and the density matrix renormalization group.

We compute physical observables such as the equation of state, chiral condensate, and quark distribution function as functions of the baryon number density.

As a physical implication, we...

Thermalization of the quark gluon plasma (QGP) created in relativistic heavy-ion collisions is a crucial theoretical question in understanding the onset of hydrodynamics, and in a broad sense, a key step to the exploration of thermalization in quantum systems.

Addressing this problem theoretically, in a first principle manner, requires a real-time, non-perturbative method. To this end, we...

We investigate the thermodynamic properties of color-superconducting two-flavor quark matter at high densities and zero temperature at next-to-leading order (NLO) in the strong coupling and the gap. Assuming that the ground state of dense quark matter is a color superconductor, we calculate the pressure and the speed of sound for two massless quark flavors. Our results show that the NLO...

This study delves into the radial oscillations of hybrid neutron stars, which possess a unique structure comprising hadronic external layers and a quark matter core. Using a density-dependent relativistic mean-field model incorporating hyperons and $\Delta$ baryons to describe hadronic matter, along with a density-dependent quark model for quark matter, we explore the ten lowest...

In this talk I will show you our recent results on the quark pairing gap in sQGP by solving the coupled Dyson-Schwinger equations for quark propagator and quark gluon vertex in the Nambu-Gorkov basis which is widely applied to study the color superconductivity. We acquire a quark pairing gap in chiral limit above the chiral phase transition temperature $T_c$. The gap persists up to...

Mass spectra of light mesons (K0, π0, η, η’) under external magnetic fields are investigated in temperature-baryon chemical potential plane by using quark model. We observe that there appear mass jumps for mesons at their Mott transitions, which are induced by the Landau levels of their constituent quarks. The critical temperature of the Mott transition shows different behaviors, which first...

In this presentation, I revisit the Dirac theory under an external magnetic field and rotation. Motivated by experimental observations of significant vorticities in heavy ion collisions, there has been active exploration into the thermodynamics of rotating QCD matter. While the pure rotational effect has received attention, the interplay between rotation and magnetic fields remains...

Fluctuations are ubiquitous phenomena emerging across all physical length scales and play a crucial role in determining properties and dynamics when the system's degrees of freedom are notably finite. Such extreme conditions can be achieved in heavy-ion collision experiments, where fluctuations are important measures of collectivity and criticality. We focus on non-equilibrium fluctuations...

The low energy QCD matter can be effectively desicrbed by O(4) model. the spontaneous breaking of approximate symmetries gives rise to emergent pseudo-Goldstone modes and a radial $\sigma$ mode. It has been proposed that the damping of pseudo-Goldstone modes at finite temperatures is universally constrained in the way that $\Omega_{\varphi}/m_{\varphi}^2\simeq D_{\varphi}$ in the broken phase,...

The difference between the spin alignments of $K^\ast$ and those of $\phi$ at the low collision energies is a puzzle raised by the recent experiments. Unlike $\phi$ meson, $K^\ast$, carrying a unit strange charge, should react to strange chemical potential $\mu_S$. In this talk, I shall first convince you that $\mu_S$ is not small in a brayon-rich medium for keeping strange neutrality, and...

We derive a Cooper-Frye-type formula for the spin alignment of spin-1 bosons at local thermal equilibrium described by a grand canonical ensemble specified by temperature, fluid velocity, and spin potential. We develop a set of Feynman rules to evaluate the Wigner function order by order in space-time gradient.

We assume that the vector mesons freeze out on a space-like hypersurface in the...

In this talk I will discuss dissociation of large-momentum charmonia with light mesons in hadronic matter. Momenta of charmonia created in Pb-Pb collisions at the CERN Large Hadron Collider are so large that three or more mesons may be produced when the charmonia collide with light mesons in hadronic matter. We study the meson-charmonium collision in a mechanism where the collision produces...

This work is based on 2+1 flavor quantum chromodynamics (QCD) calculations

within the functional renormalization group (fRG) approach. We calculate the four-fermi interaction of QCD under the Fierz-complete basis, and improve the flow equations of dynamical hadronization. We also calculate the contributions of different four-fermi channels under finite temperature and density, split the...

Equilibrium properties of strongly interacting matter are typically characterized by the quantum chromodynamics (QCD) equation of state (EoS). External factors, especially magnetic fields, can significantly influence this characterization. In efforts to delve deeper into these properties, we perform lattice simulations of $(2+1)$-flavor QCD using improved staggered quarks at the physical pion...

The extreme conditions within neutron stars provide a unique laboratory for probing QCD phases, like the crystalline colour superconducting (CCS) phase. We investigate the observable properties of hybrid stars (HSs) with a solid quark matter core in the CCS phase. These HS models are characterized by a sharp phase transition with a significant density discontinuity, which softens the equations...