Hopping parameter expansion to all orders using the complex Langevin equation

We propose two novel formulations of the hopping parameter expansion for finite density QCD using Wilson fermions, while keeping the gauge action intact. We use the complex Langevin equation to circumvent the sign problem in the theory. We perform simulations at very high order of the expansion, such that convergence is directly observable. We compare results to the full QCD results, and see agreement at sufficiently high orders. These results provide support for the use of complex Langevin dynamics to study QCD at nonzero density, both in the full and the expanded theory, and for the convergence of the latter.

Further discussion of Tomboulis approach to the confinement problem

We discuss in some detail certain gaps and open problems in the recent paper by E. T. Tomboulis, which claims to give a rigorous proof of quark confinement in 4D lattice Yang-Mills theory for all values of the bare coupling. We also discuss what would be needed to fill the gaps in his proof.

The High Density Region of QCD from an Effective Model

We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov-type loops as the main dynamical variables representing the fermionic matter. This model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the simulated Monte Carlo ensemble with the true one. We review the main features of the model and present results concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the Polykov loop susceptibility, which may be used to characterize the various phases expected at high baryonic density. In this way, we obtain information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints about the behaviour of non-zero density QCD.

A Model for QCD at High Density and Large Quark Mass

We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov type of loops as the main dynamical variables representing the fermionic matter. To get a first idea of the phase structure, the model is analyzed in strong coupling expansion and using a mean field approximation. In numerical simulations, the model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the Monte Carlo ensemble with the true one. We review the main features of the model and present calculations concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the diquark susceptibility, which may be used to characterize the various phases expected at high baryonic density. We obtain in this way information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints for the behaviour of non-zero density QCD.