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In this paper I determine the general form of the physical and mathematicalrestrictions that arise on the interactions of gravity and scalar fields in the2T field theory setting, in d+2 dimensions, as well as in the emerging shadowsin d dimensions. These constraints on scalar fields follow from an underlyingSp(2,R) gauge symmetry in phase space. Determining these general constraintsprovides a basis for the construction of 2T supergravity, as well as physicalapplications in 1T-field theory, that are discussed briefly here, and moredetail elsewhere. In particular, no scale models that lead to a vanishingcosmological constant at the classical level emerge naturally in this setting.

Constraints on Interacting Scalars in 2T Field Theory and No Scale Models in 1T Field Theory