String and Particle with Two Times

TL;DR

This paper introduces a new theoretical framework for strings and particles with two timelike dimensions, analyzing their gauge symmetries, constraints, and critical dimensions in various spacetime signatures.

Contribution

It proposes a novel action for systems with two times, explores their gauge symmetries, and determines critical dimensions for consistency in both bosonic and supersymmetric cases.

Findings

Critical dimensions are 27 or 28 for bosonic systems in flat spacetime.

Supersymmetric systems have critical dimensions 11 or 12.

Effective motion reduces to single time dimension due to gauge symmetries.

Abstract

An action for a string and a particle with two timelike dimensions is proposed and analyzed. Due to new gauge symmetries and associated constraints, the motion of each system in the background of the other is equivalent to effective motion with a single timelike dimension. The quantum constraints are consistent only in critical dimensions. For the bosonic system in flat spacetime the critical dimension is 27 or 28, with signature (25,2) or (26,2), depending on whether the particle is massive or massless respectively. For the supersymmetric case the critical dimensions are 11 or 12, with signature (9,2) or (10,2), under the same circumstances. Generalizations to multiparticles, strings and p-branes are outlined.