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A bstract A new thermal regime of QCD, featuring decoupled scale-invariant infrared glue, has been proposed to exist both in pure-glue (N f =0) and “real-world” (N f =2+1 at physical quark masses) QCD. In this IR phase , elementary degrees of freedom flood the infrared, forming a distinct component independent from the bulk. This behavior necessitates non-analyticities in the theory. In pure-glue QCD, such non-analyticities have been shown to arise via Anderson-like mobility edges in Dirac spectra ( λ IR = 0, ± λ A ≠ 0), as manifested in the dimension function d IR ( λ ). Here, we present the first evidence, based on lattice QCD calculation at a =0.105 fm, that this mechanism is also at work in real-world QCD, thus supporting the existence of the proposed IR regime in nature. An important aspect of our results is that, while at T = 234 MeV we find a dimensional jump between zero modes and lowest near-zero modes very close to unity ( d IR = 3 to d IR ≃ 2), similar to the IR phase of pure-glue QCD, at T = 187 MeV we observe a continuous λ -dependence. This suggests that thermal states just above the chiral crossover are non-analytically (in T ) connected to thermal state at T = 234 MeV, supporting the key original proposition that the transition into the IR regime occurs at a temperature strictly above the chiral crossover.

We present a lattice determination of the heavy-quark diffusion coefficient in (2+1)-flavor QCD with almost physical quark masses. The momentum and spatial diffusion coefficients are extracted for a wide temperature range, from T = 163 MeV to 10 GeV. The results are in agreement with previous works from the HotQCD collaboration, and show fast thermalization of the heavy quark inside the QGP. Near the chiral crossover temperature Tc ≃ 150 MeV, our results are close to the AdS/CFT estimation computed at strong coupling.

We calculate the temperature dependence of bottomonium correlators in (2+1)-flavor lattice QCD with the aim to constrain in-medium properties of bottomonia at high temperature. The lattice calculations are performed using HISQ action with physical strange quark mass and light quark masses twenty times smaller than the strange quark mass at two lattice spacings a = 0.0493 fm and 0.0602 fm, and temporal extents Nτ = 16 − 30, corresponding to the temperatures T = 133 − 250 MeV. We use a tadpole-improved NRQCD action including spin-dependent v6 corrections for the heavy quarks and extended meson operators in order to be sensitive to in-medium properties of the bottomonium states of interest. We find that within estimated errors the bottomonium masses do not change compared to their vacuum values for all temperatures under our consideration; however, we find different nonzero widths for the various bottomonium states.

A bstract We determine the QCD equation of state at nonzero temperature in the presence of an isospin asymmetry between the light quark chemical potentials on the lattice. Our simulations employ N f = 2 + 1 flavors of dynamical staggered quarks at physical masses, using three different lattice spacings. The main results, obtained at the individual lattice spacings, are based on a two-dimensional spline interpolation of the isospin density, from which all relevant quantities can be obtained analytically. In particular, we present results for the pressure, the interaction measure, the energy and entropy densities, as well as the speed of sound. Remarkably, the latter is found to exceed its ideal gas limit deep in the pion condensed phase, the first account of the violation of this limit in first principles QCD. Finally, we also compute the phase diagram in the temperature — isospin density plane for the first time. Even though the results are not continuum extrapolated and thus not final, the data for all observables will be useful for the benchmarking of effective theories and low-energy models of QCD and are provided in ancillary files for simple reuse.

A bstract Spectral functions encode a wealth of information about the dynamics of any given system, and the determination of their non-perturbative characteristics is a long-standing problem in quantum field theory. Whilst numerical simulations of lattice QCD provide ample data for various Euclidean correlation functions, the inversion required to extract spectral functions is an ill-posed problem. In this work, we pursue previously established constraints imposed by field locality at finite temperature T , namely that spectral functions possess a non-perturbative representation which generalises the well-known Källén-Lehmann spectral form to T > 0. Using this representation, we analyse lattice QCD data of the spatial pseudo-scalar correlator in the temperature range 220–960 MeV, and obtain an analytic expression for the corresponding spectral function, with parameters fixed by the data. From the structure of this spectral function we find evidence for the existence of a distinct pion state above the chiral pseudo-critical temperature T pc , and contributions from its first excitation, which gradually melt as the temperature increases. As a non-trivial test, we find that the extracted spectral function reproduces the corresponding temporal lattice correlator data for T = 220 MeV.

Lattice $\\mathbb{Z}$3 theories with complex actions share many key features with finite- density QCD including a sign problem and $\\mathcal{CK}$ symmetry. Complex $\\mathbb{Z}$3 spin and gauge models exhibit a generalized Kramers-Wannier duality mapping them onto chiral $\\mathbb{Z}$3 spin and gauge models, which are simulatable with standard lattice methods in large regions of parameter space. The Migdal-Kadanoff real-space renormalization group (RG) preserves this duality, and we use it to compute the approximate phase diagram of both spin and gauge $\\mathbb{Z}$3 models in dimensions one through four. Chiral $\\mathbb{Z}$3 spin models are known to exhibit a Devil’s Flower phase structure, with inhomogeneous phases that can be thought of as $\\mathbb{Z}$3 analogues of chiral spirals. Out of the large class of models we study, we find that only chiral spin models and their duals have a Devil’s Flower structure with an infinite set of inhomogeneous phases, a result we attribute to Elitzur’s theorem. We also find that different forms of the Migdal-Kadanoff RG produce different numbers of phases, a violation of the expectation for universal behavior from a real-space RG. We discuss extensions of our work to $\\mathbb{Z}$N models, SU(N) models and nonzero temperature.

A bstract We investigate the phase structure and the equation of state (EoS) for dense two-color QCD (QC 2 D) at low temperature ( T = 40 MeV, 32 4 lattice) for the purpose of extending our previous works [ 1 , 2 ] at T = 80 MeV (16 4 lattice). Indeed, a rich phase structure below the pseudo-critical temperature T c as a function of quark chemical potential μ has been revealed, but finite volume effects in a high-density regime sometimes cause a wrong understanding. Therefore, it is important to investigate the temperature dependence down to zero temperature with large-volume simulations. By performing 32 4 simulations, we obtain essentially similar results to the previous ones, but we are now allowed to get a fine understanding of the phase structure via the temperature dependence. Most importantly, we find that the hadronic-matter phase, which is composed of thermally excited hadrons, shrinks with decreasing temperature and that the diquark condensate scales as ⟨ qq ⟩ ∝ μ 2 in the BCS phase, a property missing at T = 80 MeV. From careful analyses, furthermore, we confirm a tentative conclusion that the topological susceptibility is independent of μ . We also show the temperature dependence of the pressure, internal energy, and sound velocity as a function of μ . The pressure increases around the hadronic-superfluid phase transition more rapidly at the lower temperature, while the temperature dependence of the sound velocity is invisible. Breaking of the conformal bound is also confirmed thanks to the smaller statistical error.

A bstract After motivating an interest in the shape of the topological charge density spectral function in hot Yang-Mills theories, we estimate it with the help of thermally averaged classical real-time simulations, for N c = 2 , 3. After subtracting a perturbative contribution at large frequencies, we observe a non-trivial shape at small frequencies (a dip rather than a peak), interpolating smoothly towards the sphaleron rate at zero frequency. Possible frequency scales making an appearance in this shape are discussed. Implications for warm axion inflation and reheating, and for imaginary-time lattice measurements of the strong sphaleron rate, are recapitulated.

A bstract We study topology in Quantum Chromodynamics at high temperatures by means of lattice calculations. Simulations are performed with N f = 2 + 1 + 1 Wilson twisted mass fermions at maximal twist with physical quark masses, and temperatures T ≳ 180 MeV. The results obtained with three lattice spacings ranging between 0 . 057 and 0 . 080 fm are extrapolated to the continuum limit. We compare the results for the topological susceptibility obtained with the field-theoretic definition with those obtained from an observable constructed with the disconnected part of the chiral susceptibility, and we confirm their agreement — within the largish errors — on our range of temperatures. We also study the topological charge distribution, the next order cumulant b 2 and, for the first time, the Free Energy as a function of the θ angle. We find a rapid crossover to the Dilute Instanton Gas behaviour above T ≃ 300 MeV for all the observables we have considered.

A bstract In this paper we study the Chiral Separation Effect by means of first-principles lattice QCD simulations. For the first time in the literature, we determine the continuum limit of the associated conductivity using 2+1 flavors of dynamical staggered quarks at physical masses. The results reveal a suppression of the conductivity in the confined phase and a gradual enhancement toward the perturbative value for high temperatures. In addition to our dynamical setup, we also investigate the impact of the quenched approximation on the conductivity, using both staggered and Wilson quarks. Finally, we highlight the relevance of employing conserved vector and anomalous axial currents in the lattice simulations.