New localization mechanism and Hodge duality for $q-$form field

Abstract

In this paper, we investigate the problem of localization and the Hodge duality for a $q-$form field on a $p-$brane with codimension one. By a general Kaluza-Klein (KK) decomposition without gauge fixing, we obtain two Schrödinger-like equations for two types of KK modes of the bulk $q-$form field, which determine the localization and mass spectra of these KK modes. It is found that there are two types of zero modes (the $0-$level modes): a $q-$form zero mode and a $(q-1)-$form one, which cannot be localized on the brane at the same time. For the $n-$level KK modes, there are two interacting KK modes, a massive $q-$form KK mode and a massless $(q-1)-$form one. By analyzing gauge invariance of the effective action and choosing a gauge condition, the $n-$level massive $q-$form KK mode decouples from the $n-$level massless $(q-1)-$form one. It is also found that the Hodge duality in the bulk naturally becomes two dualities on the brane. The first one is the Hodge duality between a $q-$form zero mode and a $(p-q-1)-$form one, or between a $(q-1)-$form zero mode and a $(p-q)-$form one. The second duality is between two group KK modes: one is an $n-$level massive $q-$form KK mode with mass $m_n$ and an $n-$level massless $(q-1)-$form mode; another is an $n-$level $(p-q)-$form one with the same mass $m_n$ and an $n-$level massless $(p-q-1)-$form mode. Because of the dualities, the effective field theories on the brane for the KK modes of the two dual bulk form fields are physically equivalent.

19 pages, accepted by Phys. Rev. D

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