Quantum effects of a massive 3-form coupled to a Dirac field

Abstract

We consider the coupling of A_{μνρ} to the generic current of matter field, later identified with the spin density current of a Dirac field. In fact, one of the objectives of this paper is to investigate the impact of the quantum fluctuations of A_{μνρ} on the effective dynamics of the spinor field. The consistency of the field equations, even at the classical level, requires the introduction of a mass term for A_{μνρ}. In this case, the Casimir vacuum pressure includes a contribution that is explicitly dependent on the mass of A_{μνρ} and leads us to conclude that the mass term plays the same role as the infrared cutoff needed to regularize the finite volume partition functional previously calculated in the massless case. Remarkably, even in the presence of a mass term, A_{μνρ} contains a mixture of massless and massive spin-0 fields so that the resulting equation is still gauge invariant. This is yet another peculiar, but physically relevant property of A_{μνρ} since it is reflected in the effective dynamics of the spinor fields and confirms the confining property of A_{μνρ} already expected from the earlier calculation of the Wilson loop.