Localization and mass spectrum of q -form fields on branes

Abstract

In this paper, we investigate localization of a bulk massless q-form field on codimension-one branes by using a new Kaluza-Klein (KK) decomposition, for which there are two types of KK modes for the bulk q-form field, the q-form and (q − 1)-form modes. The first modes may be massive or massless while the second ones are all massless. These two types of KK modes satisfy two Schrödinger-like equations. For a five-dimensional brane model with a finite extra dimension, the spectrum of a bulk 3-form field on the brane consists of some massive bound 3-form KK modes as well as some massless bound 2-form ones with different configuration along the extra dimension. These 2-form modes are different from those obtained from a bulk 2-form field. For a five-dimensional degenerated Bloch brane model with an infinite extra dimension, some massive 3-form resonant KK modes and corresponding massless 2-form resonant ones are obtained for a bulk 3-form field.where the field strengthq+1 ] . The 0-form and 1-form fields are just scalar and vector fields. The higher q-form fields with q ≥ 2 are new types of fields in a higher-dimensional space-time with dimension D > 4, which are used to solve some unknown problems such as the cosmological constant problem or dark energy http://dx.

Gauge invariance and localization of vector Kaluza–Klein modes

“…In Refs. [31][32][33][34] with the general KK decomposition (1) the gauge invariance of massive vector KK modes for a free bulk U(1) gauge field in branes with codimension one or more was discussed. Here we give a brief review on a brane with codimension one.…”

“…Thus it is natural to ask whether the Lagrangian of these massive vector KK modes is gauge a e-mail: fuche13@mail.xjtu.edu.cn (corresponding author) b e-mail: zhaozhh78@sdust.edu.cn c e-mail: electron1@stu.xjtu.edu.cn invariant. It was found that for a free bulk U(1) gauge field, with a gauge free KK decomposition, some scalar KK modes coupling with the vector ones appear [31][32][33][34]. Because of these scalar KK modes the massive vector ones were identified to be gauge invariant.…”

“…However, in a brane with codimension one it is difficult to localize these KK modes. It needs some kinds of localization mechanism [31,32,38,[40][41][42]45,47,48]. For example, in Ref.…”

p-Forms non-minimally coupled to gravity in Randall–Sundrum scenarios

“…The equations (20) and (25), with the potentials (21) and (26), governs the extra dimension component of KR and vector fields respectively. Now we must analyze the localization of the zero mode of the KR and vector fields.…”

Consistency conditions for p-form field localization on codimension two braneworlds

“…Among them, the U (1) vector field (1-form) and the Kalb-Ramond field (2-form) has an important status. The study of the confinement of these two fields and another p-form was already widely performed in the literature [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. There are other related issues, such as that p-form fields have been used to provide the stabilization of the radius in RS-I model [50]; or, that one introduced torsion in RS-I scenarios [51]; or still, one addressed generation of inflation or gravitational waves [52,53]; among other issues [54][55][56].…”