Abstract. We investigate 2-colour QCD with 2 flavours of Wilson fermion at nonzero temperature T and quark chemical potential µ, with a pion mass of 700 MeV (mπ/mρ = 0.8). From temperature scans at fixed µ we find that the critical temperature for the superfluid to normal transition depends only very weakly on µ above the onset chemical potential, while the deconfinement crossover temperature is clearly decreasing with µ. We find indications of a region of superfluid but deconfined matter at high µ and intermediate T . The static quark potential determined from the Wilson loop is found to exhibit a 'string tension' that increases at large µ in the 'deconfined' region. The electric (longitudinal) gluon propagator in Landau gauge becomes strongly screened with increasing temperature and chemical potential. The magnetic (transverse) gluon shows little sensitivity to temperature, and exhibits a mild enhancement at intermediate µ before becoming suppressed at large µ.PACS. 11.15Ha Lattice gauge theory -12.38Aw Lattice QCD calculations -21.65Qr Quark matter -12.38Mh Quark-gluon plasma

2-color QCD is the simplest QCD-like theory which is accessible to lattice simulations at finite density. It therefore plays an important role to test qualitative features and to provide benchmarks to other methods and models, which do not suffer from a sign problem. To this end, we determine the minimal-Landau-gauge propagators and 3-point vertices in this theory over a wide range of densities, the vacuum, and at both finite temperature and density. The results show that there is essentially no modification of the gauge sector in the low-temperature, low-density phase. Even outside this phase only mild modifications appear, mostly in the chromoelectric sector.

We study two-color QCD with two flavors of Wilson fermion as a function of quark chemical potential µ and temperature T , for two different lattice spacings and two different quark masses. We find that the quarkyonic region, where the behaviour of the quark number density and the diquark condensate are described by a Fermi sphere of almost free quarks distorted by a BCS gap, extends to larger chemical potentials with decreasing lattice spacing or quark mass. In both cases, the quark number density also approaches its non-interacting value. The pressure at low temperature is found to approach the Stefan-Boltzmann limit from below.

QCD at high chemical potential has interesting properties such as deconfinement of quarks. Two-color QCD, which enables numerical simulations on the lattice, constitutes a laboratory to study QCD at high chemical potential. Among the interesting properties of two-color QCD at high density is the diquark condensation, for which we present recent results obtained on a finer lattice compared to previous studies. The quark propagator in two-color QCD at non-zero chemical potential is referred to as the Gor'kov propagator. We express the Gor'kov propagator in terms of form factors and present recent lattice simulation results.Comment: Talk given at the conference Confinement XI, September 8-12, 2014, St. Petersburg, Russia. 8 pages, 15 figure

2-color QCD, i. e. QCD with the gauge group SU(2), is the simplest non-Abelian gauge theory without sign problem at finite quark density. Therefore its study on the lattice is a benchmark for other non-perturbative approaches at finite density. To provide such benchmarks we determine the minimal-Landau-gauge 2-point and 3-gluon correlation functions of the gauge sector and the running gauge coupling at finite density. We observe no significant effects, except for some low-momentum screening of the gluons at and above the supposed high-density phase transition. IntroductionUnderstanding the full phase diagram of QCD from first principles studies has been a challenge for decades. The most interesting phenomena occur in the strongly interacting regime, where perturbative methods fail. Therefore non-perturbative approaches like functional methods and lattice gauge theory are applied to study QCD in the different thermodynamic regimes. Unfortunately, lattice QCD suffers from the sign problem at finite density. Therefore, it does not so far seem possible to reproduce at finite density the interplay of lattice and functional methods that has proven fruitful in the finite temperature case [1]. One way to circumvent this problem is the study of QCD-like theories [2] at finite density on the lattice, which do not suffer from the sign problem. Of course, these theories need to share as many properties with real QCD as possible to be really constraining. The simplest such theory is QC 2 D, i. e. QCD with the gauge group SU(2) rather than SU(3), but otherwise left unchanged. Therefore, QC 2 D has already been extensively studied, especially using lattice methods [3][4][5][6][7][8][9][10][11]. The focus of the present contribution is on the properties of the gauge sector at finite density, especially the (minimal) Landau-gauge propagators and 3-point vertices and the running gauge coupling. These are of prime importance as inputs and/or benchmarks for functional calculations [1].Our results indicate no strong change with respect to the vacuum. Only around the supposed deconfinement phase transition and at very high density do we see the onset of a moderate screening of the gluons. If this finding would be generic, this would considerably simplify studies of finite densities using functional methods, as then the gauge sector could be left essentially as in the vacuum, as has been done, e. g., already in [12][13][14][15][16], supporting the findings in these studies. Conversely, this implies that the high-density phase remains strongly coupled in the whole range of densities studied here.

We investigate 2-colour QCD with 2 flavours of Wilson fermion at nonzero temperature T and quark chemical potential µ, with a pion mass of 700 MeV (m π /m ρ = 0.8). From temperature scans at fixed µ we find that the critical temperature for the superfluid to normal transition depends only very weakly on µ above the onset chemical potential, while the deconfinement crossover temperature is clearly decreasing with µ. We also present results for the Landau-gauge gluon propagator in the hot and dense medium.

We investigate 2-colour QCD with 2 flavours of Wilson fermion at nonzero temperature T and quark chemical potential µ, with a pion mass of 700 MeV (m π /m ρ = 0.8). From temperature scans at fixed µ we find that the critical temperature for the superfluid to normal transition depends only very weakly on µ above the onset chemical potential, while the deconfinement crossover temperature is clearly decreasing with µ. We also present results for the Landau-gauge gluon propagator in the hot and dense medium.