Two-Time Physics in Field Theory

TL;DR

This paper develops a covariant field theory in d+2 dimensions for two-time physics, establishing connections with conformal symmetry, Dirac's work, and providing a unifying framework that encompasses various lower-dimensional theories and related dualities.

Contribution

It formulates a consistent d+2 dimensional field theory for two-time physics from covariant quantization, linking it to conformal symmetry and embedding multiple d-dimensional theories.

Findings

Field theory in d+2 dimensions derived from covariant quantization.

Relation established between Dirac's conformal symmetry and two-time physics.

Higher-dimensional theory unifies various lower-dimensional field theories.

Abstract

A field theory formulation of two-time physics in d+2 dimensions is obtained from the covariant quantization of the constraint system associated with the OSp(n|2) worldline gauge symmetries of two-time physics. Interactions among fields can then be included consistently with the underlying gauge symmetries. Through this process a relation between Dirac's work in 1936 on conformal symmetry in field theory and the more recent worldline formulation of two-time physics is established while providing a worldline gauge symmetry basis for the field equations in d+2 dimensions. It is shown that the field theory formalism goes well beyond Dirac's goal of linearizing conformal symmetry. In accord with recent results in the worldline approach of two-time physics, the d+2 field theory can be brought down to diverse d dimensional field theories by solving the subset of field equations that correspond to the ``kinematic'' constraints. This process embeds the one ``time'' in d-dimensions in different ways inside the d+2 dimensional spacetime. Thus, the two-time d+2 field theory appears as a more fundamental theory from which many one-time d dimensional field theories are derived. It is suggested that the hidden symmetries and relations among computed quantities in certain d-dimensional interacting field theories can be taken as the evidence for the presence of a higher unifying structure in a d+2 dimensional spacetime. These phenomena have similarities with ideas such as dualities, AdS-CFT correspondence and holography.