Abstract
It is important to obtain (nearly) massless localized modes for the low-energy four-dimensional effective field theory in the brane-world scenario. We propose a mechanism for bosonic zero modes using the field-dependent kinetic function in the classical field theory set-up. As a particularly simple case, we consider a domain wall in five dimensions, and show that massless states for scalar (0-form), vector (1-form), and tensor (2-form) fields appear on a domain wall, which may be called topological because of robustness of their existence (insensitive to continuous deformations of parameters). The spin of localized massless bosons is selected by the shape of the nonlinear kinetic function, analogously to the chirality selection of fermion by the well-known Jackiw-Rebbi mechanism. Several explicitly solvable examples are given. We consider not only (anti)BPS domain walls in non-compact extra dimension but also non-BPS domain walls in compact extra dimension.
Highlights
A long time ago, Jackiw and Rebbi showed that massless fermions are trapped by a topological soliton, namely a domain wall [1]
As in the scalar case, the physical massless gauge field appears on the domain wall whenever βðTðyÞÞ is a square integrable
F0 is localized around the BPS domain wall at y 1⁄4 0 while f 0 is around the anti-BPS domain wall at y 1⁄4 πR for εF 1⁄4 þ1; see the third column from the left of Fig. 3. (The mode functions of zero modes are exchanged for εF 1⁄4 −1.) They are normalizable since the extra dimension is compact
Summary
A long time ago, Jackiw and Rebbi showed that massless fermions are trapped by a topological soliton, namely a domain wall [1]. The Jackiw-Rebbi mechanism naturally provides massless chiral fermions (leptons and quarks) on a domain wall (a 3-brane) in five dimensions. We will reanalyze the localization of massless gauge fields on a domain wall via the fielddependent gauge kinetic term from a different viewpoint where we do not need the speculative connection between it and confinement. Once we recognize the massless gauge fields as topological, we will show that the Jackiw-Rebbi-like mechanism for bosons works for vector (1-form) fields and for scalar (0-form) and tensor (2-form) fields. To the selection of chirality of a four-dimensional fermion by the wall, we will show the Jackiw-Rebbi-like mechanism selects the spin of localized massless bosons: It selects between four-dimensional vector or scalar (tensor or vector) in the case of fivedimensional vector (tensor) bosonic fields.
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