Kaluza-Klein mode mixing in braneworlds: constraints on scalar absorption and physical degrees of freedom

TL;DR

This paper studies how Kaluza-Klein modes mix in braneworld models, revealing constraints on warp factors, preserving gauge invariance, and showing how mixing affects scalar absorption and the physical spectrum of modes.

Contribution

It demonstrates that mode mixing imposes constraints on warp factors and affects the physical degrees of freedom in braneworld models, especially in higher-dimensional scenarios.

Findings

Gauge invariance remains despite mode mixing.

Scalar modes alter the absorption mechanism of vector KK modes.

Multiple scalar sectors in (4+2)-dimensional models lead to complex mixing dynamics.

Abstract

We investigate the mixing between Kaluza-Klein (KK) modes for a bulk U(1) gauge field within braneworld models. By demanding orthonormality and completeness for the KK basis functions, we demonstrate that the decoupling of mixed sectors, specifically of the vector-scalar and scalar-scalar types, imposes stringent constraints on the warp factors of codimension-d (d>1) backgrounds. We show that the gauge invariance of the four-dimensional effective action is preserved despite such mixing, manifesting as an intrinsic property of the massive vector KK sector. However, the generic presence of vector-scalar mixing fundamentally alters the absorption mechanism of the scalar modes, dynamically shifting the physical masses of the vector KK modes away from their unperturbed eigenvalues. In (4+2)-dimensional models, the existence of two distinct scalar sectors significantly enriches the mixing dynamics. As the massive vectors absorb only specific linear combinations of these scalars, a residual set of massive scalar KK modes persists as physical degrees of freedom.