We present a discussion of problems that have arisen in attempts to understand the behavior of lattice QCD at high densities. The effects observed in the lattice simulations do not seem to bc consistent with what we expect from the usual ideas of chiral symmetry breaking. In particular, at zero quark mass, there does not seem to be a massive baryon at finite density.

A brief summary of the formulation of QCD at finite chemical potental, µ, is presented. The failure of the quenched approximation to the problem is reviewed.Results are presented for dynamical simulations of the theory at strong and intermediate couplings. We find that the problems associated with the quenched theory persist: the onset of non-zero quark number does seem to occur at a chemical potential ≈ . However analysis of the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane, (e µ/T ), does show signals of critical behaviour in the expected region of chemical potential.Results are presented for a simulation at finite density of the Gross-Neveu model on a 16 3 lattice near to the chiral limit. Contrary to our simulations of QCD no pathologies were found when µ passed through the value mπ 2.

We study QCD at non-zero quark density, zero temperature, infinite coupling using the Glasgow algorithm. An improved complex zero analysis gives a critical point µ c in agreement with that of chiral symmetry restoration computed with strong coupling expansions, and monomer-dimer simulations.We observe, however, two unphysical critical points: the onset for the number density µ o , and µ s the saturation threshold, coincident with pathological onsets observed in past quenched QCD calculations. An analysis of the probability distributions for particle number supports our physical interpretation of the critical point µ c , and offers a new intepretation of µ o , which confirms * UKQCD Collaboration 1 its unphysical nature. The perspectives for future lattice QCD calculations of the properties of dense baryonic matter are briefly discussed.2

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The approach to the chiral limit in full QCD is investigated with a blocked Wilson fermionic action. Finite size effects prohibit taking the chiral limit on small lattices. We find that various observables expected to be influenced by chiral and finite temperature properties of the theory reveal patterns which suggest a transition to chiral-symmetry restoration and deconfinement to be the origin of the observed phenomena.PACS number(s): 12.38. Gc, 11.15.Ha, 12.38.A~ 46 3618 -