An MIT bag model on S 3

Abstract

We study an MIT bag on a three-dimensional hypersphere, S 3( L), as a model for baryons at finite density. First we construct the solutions of the free Dirac equation on S 3. We then study a model where the quarks are confined to an MIT bag occupying a sector of S 3, while the complementary sector is filled with non-perturbative vacuum. The energy and size of such a bag are studied as a function of the hypersphere radius, i.e., the average baryon density. This system, where the non-perturbative vacuum is described by a volume energy, B, does not go to a completely perturbative phase at high densities. We argue that this behaviour is related to a general instability of the MIT bag with respect to formation of small volumes of non-perturbative vacuum inside a bag and suggest additional non-volume terms for the vacuum energy to avoid this problem. This model does, however, show a transition from a three-quark to a six-quark ground state at high densities, which indicates its approach to chiral-symmetry restoration and deconfinement.