Gauge invariant effective Lagrangian for Kaluza-Klein modes

Abstract

We construct a manifestly gauge invariant Lagrangian in 3+1 dimensions for N Kaluza-Klein modes of an SU(m) gauge theory in the bulk. For example, if the bulk is 4+1, the effective theory is Πi=1N+1SU(m)i with N chiral (m¯,m) fields connecting the groups sequentially. This can be viewed as a Wilson action for a transverse lattice in x5, and is shown explicitly to match the continuum 4+1 compactified Lagrangian truncated in momentum space. Scale dependence of the gauge couplings is described by the standard renormalization group technique with threshold matching, leading to effective power law running. We also discuss the unitarity constraints, and chiral fermions.