Casimir effects in chiral bag models

We show that under chiral SU(2) × SU(2) boundary conditions of the hedgehog type, the Dirac vacuum in chiral bag models picks up non-trivial chiral terms. The chiral Casimir energy and the net flux of axial current flowing through the surface of the bag are worked out in terms of the confined Dirac propagator and their subtle relationship is discussed. It is shown that both observables are plagued with ultra-violet divergences. The chiral Casimir energy diverges logarithmically, and the flux of axial current has both a logarithmic and a linear divergence. Using asymptotic expansions closed form expressions are derived and their relevance to chiral bag phenomenology is discussed.