q-Form fields on p-branes

TL;DR

This paper presents a general method for localizing q-form fields on p-branes with one extra dimension, analyzing conditions for zero mode and bound Kaluza-Klein modes across various p-brane models.

Contribution

It introduces a universal approach for localizing q-form fields on p-branes and explores their mode spectra in different geometric configurations.

Findings

Zero modes of q-form fields localize under specific conditions.

Number of bound KK modes depends on p-brane dimension and q.

Higher q-form fields have fewer massive bound modes.

Abstract

In this paper, we give one general method for localizing any form (q-form) field on p-branes with one extra dimension, and apply it to some typical p-brane models. It is found that, for the thin and thick Minkowski branes with an infinite extra dimension, the zero mode of the q-form fields with q<(p-1)/2 can be localized on the branes. For the thick Minkowski p-branes with one finite extra dimension, the localizable q-form fields are those with q<p/2, and there are also some massive bound Kaluza-Klein modes for these q-form fields on the branes. For the same q-form field, the number of the bound Kaluza-Klein modes (but except the scalar field (q=0)) increases with the dimension of the p-branes. Moreover, on the same p-brane, the q-form fields with higher q have less number of massive bound KK modes. While for a family of pure geometrical thick p-branes with a compact extra dimension, the q-form fields with q<p/2 always have a localized zero mode. For a special pure geometrical thick p-brane, there also exist some massive bound KK modes of the q-form fields with q<p/2, whose number increases with the dimension of the p-brane.