The fermion-sign problem at finite density is a persisting challenge for Monte-Carlo simulations. Theories that do not have a sign problem can provide valuable guidance and insight for physically more relevant ones that do. Replacing the gauge group SU(3) of QCD by the exceptional group G2, for example, leads to such a theory. It has mesons as well as bosonic and fermionic baryons, and shares many features with QCD. This makes the G2 gauge theory ideally suited to study general properties of dense, strongly-interacting matter, including baryonic and nuclear Fermi pressure effects. Here we present the first-ever results from lattice simulations of G2 QCD with dynamical fermions, providing a first explorative look at the phase diagram of this QCD-like theory at finite temperature and baryon chemical potential.Finite fermion density continues to be a serious challenge for Monte-Carlo simulations due to the fermionsign problem [1,2]. The sign problem appears in many areas of physics, but is of notorious importance to dense quark systems, especially in nuclei, heavy-ion collisions, and compact stellar objects. An alternative are models and continuum methods which do not have this type of problem [3][4][5][6][7]. However, these usually require approximations, and cross checks through lattice simulations remain desirable to improve systematic reliability.To provide support from numerical simulations, two major strategies have been followed. One is to replace the baryon chemical potential by some quantity more amenable to simulations, e.g. imaginary [8][9][10] or isospin [11,12] chemical potential. The other is to replace the theory with one accessible through numerical simulations at finite density. However, such theories usually differ from the original one in more or less important aspects.One very well studied replacement of QCD for strongly interacting matter at finite density is two-color QCD [13][14][15][16][17]. In this case, the baryons are bosons instead of fermions, however. This leads to profound differences, such as Bose-Einstein condensation of a baryon superfluid with a BEC-BCS crossover at high densities instead of the usual liquid-gas transition of nuclear matter. While two-color QCD has many interesting aspects that deserve to be studied in their own right, the quantum effects due to the fermionic nature of baryons are expected to play a very significant role for nuclear matter and especially in the physics of compact stellar objects [18].Therefore, a more realistic replacement theory in this regard should contain fermionic baryons. One possibility is the strong-coupling limit [19]. In order to maintain * Electronic address: axelmaas@web.de † the connection with the continuum, however, we employ here a different theory without sign problem for Monte-Carlo simulations. It is obtained by replacing the SU(3) gauge group of QCD with the gauge group G 2 [20]. All color representations of this theory are equivalent to real ones. As a consequence the Dirac operator has an antiunitary symplectic symmetry which ...

In a recent work [1] we studied the phase structure of the Gross-Neveu (GN) model in 1 + 1 dimensions at finite number of fermion flavors N f = 2, 8, 16, finite temperature and finite chemical potential using lattice field theory. Most importantly, we found an inhomogeneous phase at low temperature and large chemical potential, quite similar to the analytically solvable N f → ∞ limit. In the present work we continue our lattice field theory investigation of the finite-N f GN model by studying the formation of baryons, their spatial distribution and their relation to the chiral condensate. As a preparatory step we also discuss a linear coupling of lattice fermions to the chemical potential.

The QCD phase diagram at densities relevant to neutron stars remains elusive, mainly due to the fermion-sign problem. At the same time, a plethora of possible phases has been predicted in models. Meanwhile G2-QCD, for which the SU (3) gauge group of QCD is replaced by the exceptional Lie group G2, does not have a sign problem and can be simulated at such densities using standard lattice techniques. It thus provides benchmarks to models and functional continuum methods, and it serves to unravel the nature of possible phases of strongly interacting matter at high densities. Instrumental in understanding these phases is that G2-QCD has fermionic baryons, and that it can therefore sustain a baryonic Fermi surface. Because the baryon spectrum of G2-QCD also contains bosonic diquark and probably other more exotic states, it is important to understand this spectrum before one can disentangle the corresponding contributions to the baryon density. Here we present the first systematic study of this spectrum from lattice simulations at different quark masses. This allows us to relate the mass hierarchy, ranging from scalar would-be-Goldstone bosons and intermediate vector bosons to the G2-nucleons and deltas, to individual structures observed in the total baryon density at finite chemical potential.

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