High Energy Physics Lattice

Dual representations are constructed for non-abelian lattice spin models with U(N) and SU(N) symmetry groups, for all N and in any dimension. These models are usually related to the effective models describing the interaction between Polyakov loops in the strong coupled QCD. The original spin degrees of freedom are explicitly integrated out and a dual theory appears to be a local theory for the dual integer-valued variables. The construction is performed for the partition function and for the most general correlation function. The latter include the two-point function corresponding to quark-anti-quark free energy and the N-point function related to the free energy of a baryon. We consider both pure gauge models and models with static fermion determinant for both the staggered and Wilson fermions with an arbitrary number of flavours. While the Boltzmann weights of such models are complex in the presence of non-zero chemical potential the dual Boltzmann weights appear to be strictly positive on admissible configurations. An essential part of this work with respect to previous studies is an extension of the dual representation to the case of 1) an arbitrary value of the temporal coupling constant in the Wilson action and 2) an arbitrary number of flavours of static quark determinants. The applications and extensions of the results are discussed in detail. In particular, we outline a possible approach to Monte-Carlo simulations of the dual theory, to the large N expansion and to the development of a tensor renormalization group.

Many Polyakov loop models can be written in a dual formulation which is free of sign problem even when a non-vanishing baryon chemical potential is introduced in the action. Here, results of numerical simulations of a dual representation of one such effective Polyakov loop model at finite baryon density are presented. We compute various local observables such as energy density, baryon density, quark condensate and describe in details the phase diagram of the model. The regions of the first order phase transition and the crossover, as well as the line of the second order phase transition, are established. We also compute several correlation functions of the Polyakov loops.

The IKKT matrix model has been conjectured to provide a promising nonperturbative formulation of superstring theory. In this model, spacetime emerges dynamically from the microscopic matrix degrees of freedom in the large-N limit, and Monte Carlo simulations of the Lorentzian version provide evidence of an emergent (3+1)-dimensional expanding space-time. In this talk, we discuss the Euclidean version of the IKKT matrix model and provide evidence of dynamical compactification of the extra dimensions via the spontaneous symmetry breaking (SSB) of the 10D rotational symmetry. We perform numerical simulations of a system with a severe complex action problem by using the complex Langevin method (CLM). The CLM suffers from the singular-drift problem and we deform the model in order to avoid it. We study the SSB pattern as we vary the deformation parameter and we conclude that the original model has an SO(3) symmetric vacuum, in agreement with previous calculations using the Gaussian expansion method (GEM). We employ the GEM to the deformed model and we obtain results consistent with the ones obtained by CLM.

The transverse and longitudinal gluon propagators in the Landau gauge are studied in the two-color lattice QCD at nonzero quark chemical potentialμq. Parameterization of the momentum dependence of the propagators is provided for all values of chemical potential under study. We find that the longitudinal propagator is infrared suppressed at nonzeroμqwith suppression increasing with increasingμq. The transverse propagator dependence onμqwas found to be opposite: it is enhanced at largeμq. It is found, respectively, that the electric screening mass is increasing while the magnetic screening mass is decreasing with increasingμq. Nice agreement between the electric screening mass computed from the longitudinal propagator and the Debye mass computed earlier from the singlet static quark-antiquark potential was found. We discuss how the dependence of the propagators on the chemical potential correlates with the respective dependence of the string tension. Additionally, we consider the difference between two propagators as a function of the momentum and make interesting observations.

In this work we present an efficient construction of baryon interpolating fields for lattice QCD computations of two and three point functions. These are essential building blocks of computations of nucleon parton distribution functions (PDFs), generalized parton distribution functions (GPDs) and transverse momentum dependent distributions functions (TMDs). Lattice QCD computations of these quantities can provide additional input to assist with the global fits on experimental data for determining TMDs, GPDs and PDFs.

The smoothing procedure known as the gradient flow that suppresses ultraviolet fluctuations of gauge fields plays an important role in lattice gauge theory calculations. In particular, this procedure is often used for high-precision scale setting and renormalization of operators. The gradient flow equation is defined on the SU(3) manifold and therefore requires geometric, or structure-preserving, integration methods to obtain its numerical solutions. We examine the properties and origins of the three-stage third-order explicit Runge-Kutta Lie group integrator commonly used in the lattice gauge theory community, demonstrate its relation to 2N-storage classical Runge-Kutta methods and explore how its coefficients can be tuned for optimal performance in integrating the gradient flow. We also compare the performance of the tuned method with two third-order variable step size methods. Next, based on the recently established connection between low-storage Lie group integrators and classical 2N-storage Runge-Kutta methods, we study two fourth-order low-storage methods that provide a computationally efficient alternative to the commonly used third-order method while retaining the convenient iterative property of the latter. Finally, we demonstrate that almost no coding effort is needed to implement the low-storage Lie group methods into existing gradient flow codes.

We present a method for efficiently finding solutions of Lüscher's quantisation condition, the equation which relates two-particle scattering amplitudes to the discrete spectrum of states in a periodic spatial volume of finite extent such as that present in lattice QCD. The approach proposed is based on an eigenvalue decomposition in the space of coupled-channels and partial-waves, which proves to have several desirable and simplifying features that are of great benefit when considering problems beyond simple elastic scattering of spinless particles. We illustrate the method with a toy model of vector-vector scattering featuring a high density of solutions, and with an application to explicit lattice QCD energy level data describingJP=1−and1+scattering in several coupled channels.

The finite temperature phase diagram of QCD with two massless quark flavors is not yet understood because of the subtle effects of anomalousUA(1)symmetry. In this work we address this issue by studying the fate of the anomalousUA(1)symmetry in2+1flavor QCD just above the chiral crossover transition temperatureTc, lowering the light quark mass towards the chiral limit along line of constant physical strange quark mass. We use the gauge configurations generated using the Highly Improved Staggered Quark (HISQ) discretization on lattice volumes323?8and563?8to study the renormalized eigenvalue spectrum of QCD with valence overlap Dirac operator. We have implemented new numerical techniques that have allowed us to measure about100-200eigenvalues of the gauge ensembles with light quark masses??.6MeV. From a detailed analysis of the dependence of the renormalized eigenvalue spectrum andUA(1)breaking observables on the light quark mass, our study suggestsUA(1)is broken atT??Tceven when the chiral limit is approached.

We investigate the lattice regularization ofN=4supersymmetric Yang-Mills theory, by stochastically computing the eigenvalue mode number of the fermion operator. This provides important insight into the non-perturbative renormalization group flow of the lattice theory, through the definition of a scale-dependent effective mass anomalous dimension. While this anomalous dimension is expected to vanish in the conformal continuum theory, the finite lattice volume and lattice spacing generically lead to non-zero values, which we use to study the approach to the continuum limit. Our numerical results, comparing multiple lattice volumes, 't Hooft couplings, and numbers of colors, confirm convergence towards the expected continuum result, while quantifying the increasing significance of lattice artifacts at larger couplings.

We study the dependence of the electric conductivity on chemical potential in finite-densitySU(2)gauge theory withNf=2flavours of rooted staggered sea quarks, in combination with Wilson-Dirac and Domain Wall valence quarks. The pion mass is reasonably small withmπ/mρ≈0.4. We concentrate in particular on the vicinity of the chiral crossover, where we find the low-frequency electric conductivity to be most sensitive to small changes in fermion density. Working in the low-density QCD-like regime with spontaneously broken chiral symmetry, we obtain an estimate of the first nontrivial coefficientc(T)of the expansion of conductivityσ(T,μ)=σ(T,0)(1+c(T)(μ/T)2+O(μ4))in powers ofμ, which has rather weak temperature dependence and takes its maximal valuec(T)≈0.10±0.07around the critical temperature. At larger densities and lower temperatures, the conductivity quickly grows towards the diquark condensation phase, and also becomes closer to the free quark result. As a by-product of our study we confirm the conclusions of previous studies with heavier pion that forSU(2)gauge theory the ratio of crossover temperature to pion massTc/mπ≈0.4atμ=0is significantly smaller than in real QCD.