Nonzero Imaginary Chemical Potential Research Articles

Non-perturbative renormalization of the QCD flavour-singlet local vector current

We compute non-perturbatively the renormalization constant of the flavour-singlet local vector current ZV in lattice QCD with 3 massless flavours. Gluons are discretized by the Wilson plaquette action while quarks by the O(a)-improved Wilson–Dirac operator. The constant ZV is fixed by comparing the expectation values (1-point functions) of the conserved and local vector currents at finite temperature in the presence of shifted boundary conditions and at non-zero imaginary chemical potential. Monte Carlo simulations with a moderate computational cost allow us to obtain ZV with an accuracy of about 8‰ for values of the inverse bare coupling constant β=6/g02 in the range 5.3≤β≤11.5.

Non-perturbative definition of the QCD energy-momentum tensor on the lattice

We present a strategy to define non-perturbatively the energy-momentum tensor in Quantum Chromodynamics (QCD) which satisfies the appropriate Ward identities and has the right trace anomaly. The tensor is defined by regularizing the theory on a lattice, and by fixing its renormalization constants non-perturbatively by suitable Ward identities associated to the Poincaré invariance of the continuum theory. The latter are derived in thermal QCD with a non-zero imaginary chemical potential formulated in a moving reference frame. A renormalization group analysis leads to simple renormalization- group-invariant definitions of the gluonic and fermionic contributions to either the singlet or the non-singlet components of the tensor, and therefore of their form factors among physical states. The lattice discussion focuses on the Wilson discretization of quark fields but the strategy is general. Specific to that case, we also carry out the analysis for the on-shell O(a)-improvement of the energy-momentum tensor. The renormalization and improvement programs profit from the fact that, as shown here, the thermal theory enjoys de-facto automatic O(a)-improvement at finite temperature. The validity of the proposal is scrutinized analytically by a study to 1-loop order in lattice perturbation theory with shifted and twisted (for quarks only) boundary conditions. The latter provides also additional useful insight for a precise non-perturbative calculation of the renormalization constants. The strategy proposed here is accessible to Monte Carlo computations, and in this sense it provides a practical way to define non-perturbatively the energy-momentum tensor in QCD.

Lattice Study of QCD Phase Structure by Canonical Approach

The canonical approach is a powerful tool to circumvent sign problem in LQCD. Although it has its own difficulties it provides opportunity to determine QCD phase transition line. Using improved Wilson fermions we calculated number density at nonzero imaginary chemical potential for confinement and deconfinement phases, restored canonical partition functions Zn and did extrapolation into the real chemical potential region. We computed the higher moments of the baryon number including the kurtosis, and compared our results with information from relativistic heavy ion collision experiments.

Dyons and Roberge - Weiss transition in lattice QCD

We study lattice QCD with $N_f=2$ Wilson fermions at nonzero imaginary chemical potential and nonzero temperature. We relate the Roberge - Weiss phase transition to the properties of dyons which are constituents of the KvBLL calorons. We present numerical evidence that the characteristic features of the spectral gap of the overlap Dirac operator as function of an angle modifying the boundary condition are determined by the $Z_3$ sector of the respective imaginary chemical potential. We then demonstrate that dyon excitations in thermal configurations could be responsible (in line with perturbative excitations) for these phenomena.

Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order

We calculate the partition function of partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order using the supersymmetry method in the formulation without a singlet particle. We include a nonzero imaginary chemical potential and show that the finite-volume corrections to the low-energy constants Σ and F for the partially quenched partition function, and hence for spectral correlation functions of the Dirac operator, are the same as for the unquenched partition function. We briefly comment on how to minimize these corrections in lattice simulations of QCD. As a side result, we show that the zero-momentum integral in the formulation without a singlet particle agrees with previous results from random matrix theory.

Determination of QCD phase diagram from the imaginary chemical potential region

We test the reliability of the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model, comparing the model result with the lattice data at nonzero imaginary chemical potential. The PNJL model with the vector-type four-quark and scalar-type eight-quark interactions reproduces the lattice data on the pseudocritical temperatures of the deconfinement and chiral phase transitions. The QCD phase diagram in the real chemical potential region is predicted by the PNJL model. The critical end point survives, even if the vector-type four-quark interaction is taken into account.

Topology and chiral random matrix theory at nonzero imaginary chemical potential

We study the effect of topology for a random matrix model of QCD at nonzero imaginary chemical potential or nonzero temperature. Nonuniversal fluctuations of Dirac eigenvalues lead to normalization factors that contribute to the $\ensuremath{\theta}$ dependence of the partition function. These normalization factors have to be canceled in order to reproduce the $\ensuremath{\theta}$ dependence of the QCD partition function. The reason for this behavior is that the topological domain of the Dirac spectrum (the region of the Dirac spectrum that is sensitive to the topological charge) extends beyond the microscopic domain at nonzero imaginary chemical potential or temperature. Such behavior could persist in certain lattice formulations of QCD.

Non-trivial critical exponents for finite temperature chiral transitions at fixed total fermion number

We analyze the finite temperature chiral restoration transition of the ( D= d+1)-dimensional Gross-Neveu model for the case of a large number of flavors and fixed total fermion number. This leads to the study of the model with a nonzero imaginary chemical potential. In this formulation of the theory, we have obtained that, in the transition region, the model is described by a chiral conformal field theory where the concepts of dimensional reduction and universality do apply due to a transmutation of statistics which makes fermions act as if they were bosons, having zero energy. This result should be generic for theories with dynamical symmetry breaking, such as Quantum Chromodynamics.