On the Kalb-Ramond field with non-minimal coupling to gravity

TL;DR

This paper investigates the effects of non-minimal gravitational couplings on a massive Kalb-Ramond field, revealing strong coupling and instability issues, and explores disformal coupling as a potential remedy.

Contribution

It provides a detailed analysis of non-minimal couplings of the Kalb-Ramond field to gravity, highlighting strong coupling and instability phenomena, and proposes disformal coupling as a possible solution.

Findings

Coupling with Ricci scalar causes strong coupling of pseudo-vector modes.

Coupling with Ricci or Riemann tensor leads to strong coupling of tensor modes.

In homogeneous space-time, Ricci and Riemann couplings induce runaway instability.

Abstract

We consider a massive Kalb-Ramond field with a general non-minimal coupling to gravity. We first study the theory in flat space-time, taking into account the non-linearities. We show that the coupling with the Ricci scalar gives rise to the strong coupling of the two transverse pseudo-vector degrees of freedom, which are absent in the massless theory. We then show that if the theory is instead coupled to the Ricci tensor or the Riemann tensor, the two tensor modes become strongly coupled in addition to the transverse pseudo-vector modes. We then extend our analysis to homogeneous and isotropic space-time, with vanishing background value of the Kalb-Ramond field. We show that in this case, the couplings with the Ricci and Riemann tensor give rise to the runaway instability. Finally, we discuss the inclusion of the disformal coupling as a possible resolution to this unnatural behavior.