Bulk Kalb-Ramond field in Randall Sundrum scenario

TL;DR

This paper explores the behavior of a Kalb-Ramond tensor field in a Randall-Sundrum model, analyzing its classical solutions, mass spectrum, and interactions, revealing suppressed couplings compared to gravity.

Contribution

It provides the first detailed analysis of a gauge-invariant Kalb-Ramond field with a topological term in a Randall-Sundrum scenario, including classical solutions and phenomenological implications.

Findings

Classical solutions are self-dual or anti-selfdual, preserving parity.

Massive modes are in the TeV range and potentially detectable.

Couplings of torsion modes are suppressed relative to gravity.

Abstract

We have considered the most general gauge invariant five-dimensional action of a second rank antisymmetric Kalb-Ramond tensor gauge theory, including a topological term of the form $\epsilon^{ABLMN}B_{AB}H_{LMN}$ in a Randall-Sundrum scenario. Such a tensor field $B_{AB}$ (whose rank-3 field strength tensor is $H_{LMN}$), which appears in the massless sector of a heterotic string theory, is assumed to coexist with the gravity in the bulk. The third rank field strength corresponding to the Kalb-Ramond field has a well-known geometric interpretation as the spacetime torsion. The only non-trivial classical solutions corresponding to the effective four-dimensional action are found to be self-dual or anti-selfdual Kalb-Ramond fields. This ensures that the four-dimensional effective action on the brane is parity-conserving. The massive modes for both cases, lying in the TeV range, are related to the fundamental parameters of the theory. These modes can be within the kinematic reach of forthcoming TeV scale experiments. However, the couplings of the massless as well as massive Kalb-Ramond modes with matter on the visible brane are found to be suppressed vis-a-vis that of the graviton by the warp factor, whence the conclusion is that both the massless and the massive torsion modes appear much weaker than curvature to an observer on the visible brane.