Two-time physics in field theory

A field theory formulation of two-time physics in $d+2\mathrm{}$ dimensions is obtained from the covariant quantization of the constraint system associated with the $\mathrm{OSp}\left(n|2\right)$ 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 $d+2\mathrm{}$ 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 $d+2\mathrm{}$ 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 $\mathrm{}(d+2\mathrm{})\mathrm{}$-dimensional spacetime. Thus, the two-time $d+2\mathrm{}$ 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 evidence for the presence of a higher unifying structure in a $\mathrm{}(d+2\mathrm{})\mathrm{}$-dimensional spacetime. These phenomena have similarities with ideas such as dualities, AdS-CFT correspondence, and holography.