Two-time physics with gravitational and gauge field backgrounds

It is shown that all possible gravitational, gauge and other interactions experienced by panicles in ordinary d dimensions (one time) can be described in the language of two-time physics in a spacetime with d + 2 dimensions. This is obtained by generalizing the world line formulation of two-time physics by including background fields. A given two-time model, with a fixed set of background fields, can be gauged fixed from d + 2 dimensions to (d - 1) + 1 dimensions to produce diverse one-time dynamical models, all of which are dually related to each other under the underlying gauge symmetry of the unified two-time theory. To satisfy the gauge symmetry of the two-time theory the background fields must obey certain coupled differential equations that are generally covariant and gauge invariant in the target (d + 2)-dimensional spacetime. The gravitational background obeys a closed homothety condition while the gauge field obeys a differential equation that generalizes a similar equation derived by Dirac in 1936. Explicit solutions to these coupled equations show that the usual gravitational, gauge, and other interactions in d dimensions may be viewed as embedded in the higher (d + 2)-dimensional space, thus displaying higher spacetime symmetries that otherwise remain hidden.