Weak-coupling Calculations Research Articles

Role of electromagnetic gauge-field fluctuations in the selection between chiral and nematic superconductivity

Motivated by the observation of nematic superconductivity in several systems, we revisit the problem of the leading pairing instability of two-component unconventional superconductors on the triangular lattice -- such as $(p_{x},\,p_{y})$-wave and $(d_{x^{2}-y^{2}},\,d_{xy})$-wave. Such a system has two possible superconducting states: the chiral state (e.g. $p+ip$ or $d+id$), which breaks time-reversal symmetry, and the nematic state (e.g. $p+p$ or $d+d$), which breaks the threefold rotational symmetry of the lattice. Weak-coupling calculations generally favor the chiral over the nematic superconducting state, raising the question of what mechanism can stabilize the latter. Here, we show that the electromagnetic field fluctuations can play a crucial role in selecting between these two states. Specifically, we derive and analyze the effective free energy for the two-component superconducting order parameter after integrating out the gauge-field fluctuations, which is formally justified if the spatial order parameter fluctuations can be neglected. A non-analytic cubic term arises, as in the case of a conventional $s$-wave superconductor. However, unlike the latter, the cubic term depends on the relative phase and on the relative amplitudes between the two order parameter components, in such a way that it generally favors the nematic state. This result is a direct consequence of the fact that the stiffness of the superconducting order parameter is not isotropic. Competition with the quartic term, which favors the chiral state, leads to a renormalized phase diagram in which the nematic state displaces the chiral state over a wide region in the parameter space. We analyze the stability of the fluctuation-induced nematic phase, generalize our results to tetragonal lattices, and discuss their applicability to candidate nematic superconductors, including twisted bilayer graphene.

Sphaleron transition rates and the chiral magnetic effect

The chiral magnetic effect is a novel quantum phenomenon proposed for high-energy nuclear collisions but which has yet to be observed. We quantify the axial charge relaxation time, due to sphalerons, which enters in simulations of this effect. An extrapolation of weak coupling calculations of the sphaleron rate yields rather different relaxation times than strong coupling AdS/CFT calculations. The AdS/CFT relaxation time is the larger one of the two by an order of magnitude, but the weak coupling relaxation time may not be reliable because it is only marginally bigger than the microscopic thermalization time. The role of quark masses has yet to be accurately assessed.

Rate of photon production in the quark-gluon plasma from lattice QCD

We calculate the thermal rate of real-photon production in the quark-gluon plasma at a temperature of $T=254$ MeV using lattice QCD. The calculation is based on the difference between the spatially transverse and longitudinal parts of the polarization tensor, which has the advantage of falling off rapidly at large frequencies. We obtain this linear combination in the time-momentum representation from lattice QCD with two flavors of quarks in the continuum limit with a precision of about two parts per mille. Applying a theoretically motivated fit ansatz for the associated spectral function, we obtain values for the photon rate that are in line with QCD weak-coupling calculations; for photon momenta $ 1.0\leq k[{\rm GeV}]\leq 1.4$, our non-perturbative results constrain the rate to be no larger than twice the weak-coupling prediction. We also provide a physics interpretation of the electromagnetic spectral functions valid for all frequencies and momenta.

Color screening in ( 2+1 )-flavor QCD

We study correlation functions of spatially separated static quark-antiquark pairs in (2+1)-flavor QCD in order to investigate onset and nature of color screening at high temperatures. We perform lattice calculations in a wide temperature range, $140 \le T \le 5814\,{\rm MeV}$, using the highly improved staggered quark action and several lattice spacings to control discretization effects. By comparing at high temperatures our lattice results to weak-coupling calculations as well as to the zero temperature result for the energy of a static quark-antiquark pair, we observe that color screening sets in at $rT \approx 0.3$. Furthermore, we also observe that in the range $0.3 \lesssim r T \lesssim 0.6$ weak-coupling calculations in the framework of suitable effective field theories provide an adequate picture of color screening.

Equation of state in 2+1 flavor QCD at high temperatures

We calculate the Equation of State at high temperatures in 2+1 flavor QCD using the highly improved staggered quark action. We study the lattice spacing dependence of the pressure at high temperatures using lattices with temporal extent $N_{\tau}=6,~8,~10$ and $12$ and perform continuum extrapolations. We also give a continuum estimate for the Equation of State up to temperatures $T=2$ GeV, which are then compared with results of the weak-coupling calculations. We find a reasonably good agreement with the weak-coupling calculations at the highest temperatures.

Currents and fluctuations of quantum heat transport in harmonic chains

Heat transport in open quantum systems is particularly susceptible to the modeling of system–reservoir interactions. It thus requires us to consistently treat the coupling between a quantum system and its environment. While perturbative approaches are successfully used in fields like quantum optics and quantum information, they reveal deficiencies—typically in the context of thermodynamics, when it is essential to respect additional criteria such as fluctuation-dissipation theorems. We use a non-perturbative approach for quantum dissipative dynamics based on a stochastic Liouville–von Neumann equation to provide a very general and extremely efficient formalism for heat currents and their correlations in open harmonic chains. Specific results are derived not only for first- but also for second-order moments, which requires us to account for both real and imaginary parts of bath–bath correlation functions. Spatiotemporal patterns are compared with weak coupling calculations. The regime of stronger system–reservoir couplings gives rise to an intimate interplay between reservoir fluctuations and heat transfer far from equilibrium.

Polyakov loop in2+1flavor QCD from low to high temperatures

We study the free energy of a static quark in QCD with 2+1 flavors in a wide temperature region, 116 MeV $< T < $ 5814 MeV, using the highly improved staggered quark (HISQ) action. We analyze the transition region in detail, obtain the entropy of a static quark, show that it peaks at temperatures close to the chiral crossover temperature and also revisit the temperature dependence of the Polyakov loop susceptibilities using gradient flow. We discuss the implications of our findings for the deconfinement and chiral crossover phenomena at physical values of the quark masses. Finally a comparison of the lattice results at high temperatures with the weak-coupling calculations is presented.

Debye screening mass near deconfinement from holography

In this paper the smallest thermal screening mass associated with the correlator of the $CT$-odd operator, $\sim {\rm Tr}F_{\mu\nu}\tilde{F}^{\mu\nu}$, is determined in strongly coupled non-Abelian gauge plasmas which are holographically dual to non-conformal, bottom-up Einstein+scalar gravity theories. These holographic models are constructed to describe the thermodynamical properties of $SU(N_c)$ plasmas near deconfinement at large $N_c$ and we identify this thermal mass with the Debye screening mass $m_D$. In this class of non-conformal models with a first order deconfinement transition at $T_c$, $m_D/T$ displays the same behavior found for the expectation value of the Polyakov loop (which we also compute) jumping from zero below $T_c$ to a nonzero value just above the transition. In the case of a crossover phase transition, $m_D/T$ has a minimum similar to that found for the speed of sound squared $c_s^2$. This holographic framework is also used to evaluate $m_D$ as a function of $\eta/s$ in a strongly coupled conformal gauge plasma dual to Gauss-Bonnet gravity. In this case, $m_D/T$ decreases with increasing $\eta/s$ in accordance with extrapolations from weak coupling calculations.

Heavy flavour in nucleus-nucleus collisions at RHIC and LHC: a Langevin approach

A snapshot of the results for heavy-flavour observables in heavy-ion (AA) collisions at RHIC and LHC obtained with our transport calculations is displayed. The initial charm and beauty production is simulated through pQCD tools (POWHEG+PYTHIA) and is validated through the comparison with data from pp collisions. The propagation of c and b quarks in the medium formed in heavy-ion collisions is studied through a transport setup based on the relativistic Langevin equation. With respect to past works we perform a more systematic study, providing results with different choices of transport coefficients, either from weak-coupling calculations or from lattice-QCD simulations. Our findings are compared to a rich set of experimental data (D-mesons, non-photonic electrons, non-prompt J/\psi's) which have meanwhile become accessible.

R-mode instability in quark stars with a crystalline crust

The r-mode instability, believed to limit the rotation speed of compact stars, can provide empirical confirmation for the existence of stable deconfined phases of quark matter that are predicted by weak coupling calculations in Quantum Chromodynamics. We construct a model for strange quark stars as heavy as 2 solar masses that are made of superconducting quark matter in the bulk and a thin crystalline quark matter crust. This crystalline quark crust is sufficiently robust to withstand r-mode heating and viscous rubbing for realistic mode amplitudes O(10^{-2}), unlike a crust made of neutron-rich nuclei. The dissipation provided by viscous rubbing at the core-crust boundary is both necessary and sufficient to obtain stable rotation speeds that are consistent with the majority of rapidly spinning pulsars in low mass X-ray binaries. Our analysis implies that while bare strange stars are ruled out by the existence of rapidly spinning pulsars, a strange star with a quark matter crust is a distinct possibility.

Quark number susceptibilities at high temperatures

We calculate second and fourth order quark number susceptibilities for 2+1 flavor QCD in the high temperature region. In our study we use two improved staggered fermion formulations, namely the highly improved staggered quark formulation, and the so-called p4 formulation, as well as several lattice spacings. Second order quark number susceptibilities are calculated using both improved staggered fermion formulations, and we show that in the continuum limit the two formulations give consistent results. The fourth order quark number susceptibilities are studied only using the p4 formulation and at non-zero lattice spacings. We compare our results on quark number susceptibilities with recent weak coupling calculations, and find that these agree reasonably well with the lattice calculations within the estimated uncertainties.

Holographic Rényi entropies at finite coupling

We compute R\'enyi entropies for a spherical entangling surface in four-dimensional N=4 super-Yang-Mills at strong coupling using the AdS/CFT correspondence. Incorporating the effects of the leading \alpha' corrections to the low energy effective action of type IIB string theory, we calculate the leading corrections in inverse powers of the 't Hooft coupling (and the number of colours). The results are compared with known weak coupling calculations. Setting the order of the R\'enyi entropy q to one, it reduces to the entanglement entropy and the strong and weak coupling results match without any corrections, as expected. In the limit of q going to 0, the relation between the strong and weak coupling entropies is connected to the known corrections for the thermal free energy in flat space. We also compute the correction to the scaling dimension of twist operators.

Clustering of color sources and the shear viscosity of the QGP in heavy ion collisions at RHIC and LHC energies

The Color String Percolation Model (CSPM) is used to determine the shear viscosity to entropy ratio ($\eta/s$) of the Quark-Gluon Plasma (QGP) produced in Au-Au collisions at $\sqrt{s_{NN}}$ = 200 GeV at RHIC and Pb-Pb at $\sqrt{s_{NN}}$ = 2.76 TeV at LHC. The relativistic kinetic theory relation for $\eta/s$ is evaluated using CSPM values for the temperature and the mean free path of the QGP constituents. The experimental charged hadron transverse momentum spectrum is used to determine the percolation density parameter $\xi$ in Au-Au collisions (STAR). For Pb-Pb at $\sqrt{s_{NN}}$ = 2.76 TeV $\xi$ values are obtained from the extrapolation at RHIC energy. The value of $\eta/s$ is 0.204$\pm$0.020 and 0.262$\pm$0.026 at the CSPM initial temperatures of 193.6$\pm$3 MeV (RHIC) and 262.2 $\pm$13 MeV (LHC) respectively. These values are 2.5 and 3.3 times the AdS/CFT conjectured lower bound $1/4\pi$. We compare the CSPM $\eta/s$ analytic expression with weak coupling (wQGP) and strong coupling (sQGP) calculations. This indicates that the QGP is a strongly coupled fluid in the phase transition region.

Universality of Phases in QCD and QCD-like Theories

We argue that the whole or the part of the phase diagrams of QCD and QCD-like theories should be universal in the large-N_c limit through the orbifold equivalence. The whole phase diagrams, including the chiral phase transitions and the BEC-BCS crossover regions, are identical between SU(N_c) QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon chemical potential. Outside the BEC-BCS crossover region in these theories, the phase diagrams are also identical to that of SU(N_c) QCD at finite baryon chemical potential. We give examples of the universality in some solvable cases: (i) QCD and QCD-like theories at asymptotically high density where the controlled weak-coupling calculations are possible, (ii) chiral random matrix theories of different universality classes, which are solvable large-N (large volume) matrix models of QCD. Our results strongly suggest that the chiral phase transition and the QCD critical point at finite baryon chemical potential can be studied using sign-free theories, such as QCD at finite isospin chemical potential, in lattice simulations.

Holographic anomalous conductivities and the chiral magnetic effect

We calculate anomaly induced conductivities from a holographic gauge theory model using Kubo formulas, making a clear conceptual distinction between thermodynamic state variables such as chemical potentials and external background fields. This allows us to pinpoint ambiguities in previous holographic calculations of the chiral magnetic conductivity. We also calculate the corresponding anomalous current three-point functions in special kinematic regimes. We compare the holographic results to weak coupling calculations using both dimensional regularization and cutoff regularization. In order to reproduce the weak coupling results it is necessary to allow for singular holographic gauge field configurations when a chiral chemical potential is introduced for a chiral charge defined through a gauge invariant but non-conserved chiral density. We argue that this is appropriate for actually addressing charge separation due to the chiral magnetic effect.

Holographic Chiral Currents in a Magnetic Field

In the presence of a quark chemical potential, a magnetic field induces an axial current in the direction of the magnetic field. We compute this current in the Sakai-Sugimoto model, a holographic model which, in a certain limit, is dual to large-N_c QCD. We also compute the analogous vector current, for which an axial chemical potential is formally introduced. This vector current can potentially be observed via charge separation in heavy-ion collisions. After implementing the correct axial anomaly in the Sakai-Sugimoto model we find an axial current in accordance with previous studies and a vanishing vector current, in apparent contrast to previous weak-coupling calculations.

Steady-state current transfer and scattering theory

The correspondence between the steady-state theory of current transfer and scattering theory in a system of coupled tight-binding models of one-dimensional wires is explored. For weak interwire coupling both calculations give nearly identical results, except at singular points associated with band edges. The effect of decoherence in each of these models is studied using a generalization of the Liouville-von Neuman equation suitable for steady-state situations. An example of a single impurity model is studied in detail, leading to a lattice model of scattering off target that affects both potential scattering and decoherence. For an impurity level lying inside the energy band, the transmission coefficient diminishes with increasing dephasing rate, while the opposite holds for impurity energy outside the band. The efficiency of current transfer in the coupled wire system decreases with increasing dephasing.

Instabilities of Non-Abelian Vortices in Dense QCD

We construct a low-energy effective theory describing non-abelian vortices in the color superconducting quark matter under stress. We demonstrate that all the vortices are radically unstable against decay into the only one type of vortices due to the potential term induced by the explicit flavor symmetry breaking by the strange quark mass. A simple analytical estimate for the lifetime of unstable vortices is provided under the controlled weak-coupling calculations. We briefly discuss the (non)existence of magnetic monopoles at high density.

Classical and quantum gravity of brane black holes

We test the holographic conjecture of brane black holes: that a full classical 5D solution will correspond to a quantum corrected 4D black hole. Using the Schwarzschild-AdS black string, we compare the braneworld back reaction at strong coupling with the calculation of the quantum stress tensor on Schwarzschild-AdS4 at weak coupling. The two calculations give different results and provide evidence that the stress tensor at strong coupling is indeed different to the weak coupling calculations, and hence does not conform to our notion of a quantum corrected black hole. We comment on the implications for an asymptotically flat black hole.

P1/2hole states in odd-ANa nuclei

Simple weak-coupling calculations for {sup 23,25,27}Na demonstrate that the lowest J=1/2 proton-hole state should lie near 5 MeV in {sup 27}Na.