Field localization and the Nambu–Jona-Lasinio mass generation mechanism in an alternative five-dimensional brane model

Abstract

This proceedings is from a talk given at the APS DPF 2013 on a 5dimensional brane world model. This alternative brane world model is formally related but physically distinct from the Randall-Sundrum brane world model. The spin dependent localization of 5D fields for the alternative model are different and in some ways superior to the Randall-Sundrum. The alternative model also exhibits a cutoff in the localization of massive scalar fields not seen in the Randall-Sundrum model. This revision includes a correction to the integrand for the scalar field action appearing in the principle reference [1].

Field localization in a modified Randall-Sundrum brane model

“…Thus we can say that (3) is a modified Randall-Sundrum metric. In fact we can obtain (3) from (1) through (dy) 2 =exp( 2k|r|)(dr) 2 and exp( k|r|)dX =exp( k|y|) dx [11]. Spacetimes defined by the metrics (1) and (2) are similar, their proper distances along the extra dimension is infinite.…”

“…Both integrals depend on 0 (r). This function is the solution of the equation of motion of the field in the bulk and has the form [11] (6) Inserting the above solution into the r-integrals in (5) one can conclude that: 1) for the massless mode the field is localized on the brane only for decreasing warp factor (k>0) with b 0 =0, 2) for the massive mode the field is localized for both decreasing and increasing warp factors when we set c 0 =0. This is better localization as compared to the original RandallSundrum model where massive scalar field cannot be confined.…”

“…Unlike the metric (1) this metric has the same warp factor for all coordinates, but it does not have an exponential form. We can define a new metric which is conformally flat like (2) but with an exponential warp factor like (1) [11] 2 2 || ( ) .…”

“…In the above, M are the curved space Dirac matrices and for the corresponding metric, the covariant derivative D M are [11] 5 , . …”

“…The fine tuning of the metrics (1) and (2), i.e. setting the cosmological constant = k 2 , leads to the vanishing of the energy-momentum tensors in the bulk for metrics (1) and (2) but not for metric (3) [11,12].…”