Dimensional reduction and BRST approach to the description of a Regge trajectory

TL;DR

The paper develops a BRST-quantization framework for free Regge trajectories by performing dimensional reduction from a massless $D+1$-dimensional theory. An auxiliary Fock space and a set of constraints $L_0,L_{\pm1},L_{\pm2}$ are used to build a nilpotent BRST charge, yielding a local Lagrangian that describes an infinite tower of higher-spin states with a linear spin–mass relation $m^2=\alpha_0+n\alpha'$. Dimensional reduction to $D$ dimensions produces the Regge spectrum and its daughter trajectories, with explicit low-spin examples ($n=0,1,2$) illustrating the field content and gauge structure. The approach clarifies how locality and correct physical content emerge in the BRST treatment of higher spins and sets the stage for extensions to single-trajectory or interacting theories. It also highlights the role of second-class constraints and auxiliary variables in organizing the Regge tower.

Abstract

The local free field theory for Regge trajectory is described in the framework of the BRST - quantization method. The corresponding BRST - charge is constructed with the help of the method of dimensional reduction.