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.

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.

The inner structure of neutron stars is still an open question. One obstacle is the infamous sign problem of lattice QCD, which bars access to the high-density equation of state. A possibility to make progress and understand the qualitative impact of gauge interactions on the neutron star structure is to study a modified version of QCD without the sign problem. In the modification studied here the gauge group of QCD is replaced by the exceptional Lie group G 2 , which keeps neutrons in the spectrum. Using an equation of state from lattice calculations only we determine the mass-radius-relation for a neutron star using the Tolman-Oppenheimer-Volkoff equation. This allows us to understand the challenges and approximations currently necessary to use lattice data for this purpose. We discuss in detail the particular uncertainties and systematic problems of this approach.