Universal Aspects of $U(1)$ Gauge Field Localization on Branes in $D$-dimensions

TL;DR

This paper demonstrates that $U(1)$ gauge fields can be universally localized on branes in arbitrary $D$-dimensional spacetimes with asymptotically AdS geometry, independent of specific warp factors, and confirms the confinement of gauge and scalar sectors.

Contribution

It provides an analytical, warp-factor-independent solution for gauge field localization on branes, establishing universal conditions and extending to scalar components with boundary condition analysis.

Findings

Localization requires asymptotically AdS bulk geometry.

The solution is valid for any warp factor.

Both gauge and scalar fields can be localized under certain conditions.

Abstract

In this work, we study the general properties of the $D$-vector field localization on $(D-d-1)$-brane with co-dimension $d$. We consider a conformally flat metric with the warp factor depending only on the transverse extra dimensions. We employ the geometrical coupling mechanism and find an analytical solution for the $U(1)$ gauge field valid for any warp factor. Using this solution we find that the only condition necessary for localization is that the bulk geometry is asymptotically AdS. Therefore, our solution has an universal validity for any warp factor and is independent of the particular model considered. We also show that the model has no tachyonic modes. Finally, we study the scalar components of the $D$-vector field. As a general result, we show that if we consider the coupling with the tensor and the Ricci scalar in higher co-dimensions, there is an indication that both sectors will be localized. As a concrete example, the above techniques are applied for the intersecting brane model. We obtain that the branes introduce boundary conditions that fix all parameters of the model in such a way that both sectors, gauge and scalar fields, are confined.