Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics

Abstract

Fefferman and Graham showed some time ago that four dimensional conformal geometries could be analyzed in terms of six dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently it was shown how conformal geometry provides a description of physics manifestly invariant under local choices of unit systems. Strikingly, Einstein's equations are then equivalent to the existence of a parallel scale tractor (a six component vector subject to a certain first order covariant constancy condition at every point in four dimensional spacetime). These results suggest a six dimensional description of four dimensional physics, a viewpoint promulgated by the two times physics program of Bars. The Fefferman--Graham construction relies on a triplet of operators corresponding, respectively to a curved six dimensional light cone, the dilation generator and the Laplacian. These form an sp(2) algebra which Bars employs as a first class algebra of constraints in a six-dimensional gauge theory. In this article four dimensional gravity is recast in terms of six dimensional quantum mechanics by melding the two times and tractor approaches. This "parent" formulation of gravity is built from an infinite set of six dimensional fields. Successively integrating out these fields yields various novel descriptions of gravity including a new four dimensional one built from a scalar doublet, a tractor vector multiplet and a conformal class of metrics.

27 pages, LaTeX

References in corpus (8)

• Six-dimensional Methods for Four-dimensional Conformal Field Theories
• Quantum Mechanics in Phase Space
• Tractors, Mass and Weyl Invariance
• Gravity in 2T-Physics
• Gauge Symmetry in Phase Space, Consequences for Physics and Spacetime
• Interacting Two-Time Physics Field Theory With a BRST Gauge Invariant Action
• Unfolded form of conformal equations in M dimensions and o(M+2)-modules
• The so(d+2,2) Minimal Representation and Ambient Tractors: the Conformal Geometry of Momentum Space

Cited by in corpus (22)

• Galileons as Wess-Zumino Terms
• Non-linear Realizations of Conformal Symmetry and Effective Field Theory for the Pseudo-Conformal Universe
• Massive Higher Spins from BRST and Tractors
• Superembedding methods for 4d N=1 SCFTs
• Type-B Formal Higher Spin Gravity
• 6d conformal gravity
• Conformal bridge between asymptotic freedom and confinement
• Anomalous conformal currents, shadow fields and massive AdS fields
• Smooth metric measure spaces, quasi-Einstein metrics, and tractors
• Gauge invariant approach to low-spin anomalous conformal currents and shadow fields
• Constraints on Interacting Scalars in 2T Field Theory and No Scale Models in 1T Field Theory
• Generalized Dualities in 1T-Physics as Holographic Predictions from 2T-Physics
• A toy model for background independent string field theory
• Light-cone gauge approach to arbitrary spin fields, currents, and shadows
• A first-order approach to conformal gravity
• Quantum Mechanics and Hidden Superconformal Symmetry
• Extended hamiltonian action for arbitrary spin fields in flat and AdS spaces
• Is Quantum Gravity a Chern-Simons Theory?
• Conformal totally symmetric arbitrary spin fermionic fields
• Fundamental constraints on two-time physics
• Quantum Gravity and Causal Structures: Second Quantization of Conformal Dirac Algebras
• Einstein gravity as a gauge theory for the conformal group