Geometry and symmetry structures in two-time gravity

Journal Article · Wed Apr 15 00:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.79.085021· OSTI ID:21308357

Bars, Itzhak; Chen, S -H ^[1]

---

1. Department of Physics and Astronomy University of Southern California, Los Angeles, California 90089-2535 (United States)

Two-time (2T) gravity in d+2 dimensions predicts 1T general relativity in d dimensions, augmented with a local scale symmetry known as the Weyl symmetry in 1T field theory. The emerging general relativity comes with a number of constraints, particularly on scalar fields and their interactions in 1T field theory. These constraints, detailed in this paper, are footprints of 2T gravity and could be a basis for testing 2T physics. Some of the conceptually interesting consequences of the 'accidental' Weyl symmetry include that the gravitational constant emerges from vacuum values of the dilaton and other Higgs-type scalars and that it changes after every cosmic phase transition (inflation, grand unification, electroweak phase transition, etc.). We show that this consequential Weyl symmetry in d dimensions originates from coordinate reparametrization, not from scale transformations, in the d+2 spacetime of 2T gravity. To recognize this structure we develop in detail the geometrical structures, curvatures, symmetries, etc. of the d+2 spacetime which is restricted by a homothety condition derived from the action of 2T gravity. Observers that live in d dimensions perceive general relativity and all degrees of freedom as shadows of their counterparts in d+2 dimensions. Kaluza-Klein type modes are removed by gauge symmetries and constraints that follow from the 2T-gravity action. However some analogs to Kaluza-Klein modes, which we call 'prolongations' of the shadows into the higher dimensions, remain but they are completely determined, up to gauge freedom, by the shadows in d dimensions.

• OSTI ID: 21308357
• Journal Information: Physical Review. D, Particles Fields, Vol. 79, Issue 8; Other Information: DOI: 10.1103/PhysRevD.79.085021; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COORDINATES
DEGREES OF FREEDOM
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
GRAND UNIFIED THEORY
GRAVITATION
HIGGS BOSONS
HIGGS MODEL
INTERACTIONS
KALUZA-KLEIN THEORY
PHASE TRANSFORMATIONS
QUANTUM FIELD THEORY
SCALAR FIELDS
SPACE-TIME
SYMMETRY
TRANSFORMATIONS