High spin gauge fields and two-time physics

Abstract

All possible interactions of a point particle with background electromagnetic, gravitational and higher-spin fields are considered in the two-time physics worldline formalism in $(d,2)$ dimensions. This system has a counterpart in a recent formulation of two-time physics in noncommutative field theory with local Sp(2) symmetry. In either the worldline or field theory formulation, a general Sp(2) algebraic constraint governs the interactions, and determines the equations that the background fields of any spin must obey. The constraints are solved in the classical worldline formalism $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Elzxh}}0$ limit) as well as in the field theory formalism (all powers of $\ensuremath{\Elzxh}).$ The solution in both cases coincide for a certain 2T to 1T holographic image which describes a relativistic particle interacting with background fields of any spin in $(d\ensuremath{-}1,1)$ dimensions. Two disconnected branches of solutions exist, which seem to have a correspondence as massless states in string theory, one containing low spins in the zero Regge slope limit, and the other containing high spins in the infinite Regge slope limit.