Local gravity theories in conformal superspace

Journal Article · Mon Oct 15 04:00:00 EDT 2018 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2018.05.014· OSTI ID:22848367

Gomes, Henrique ^[1]

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1. Perimeter Institute for Theoretical Physics, 31 Caroline Street, ON, N2L 2Y5 (Canada)

The conformal method for the initial value formulation of GR is one of the most powerful and widely usedtools in both analytical studies and numerical simulations of solutions. As is well-known, it exploits a hidden spatial conformal symmetry that can be extracted from the equations. But why conformal symmetry? Motivated by these questions and by well-known obstacles to quantum gravity, I look for the most general geometrodynamical symmetries compatible with a reduced physical configuration space for metric gravity. I argue that they are indeed spatial conformal diffeomorphisms. The next question is: what sort of theories most naturally incorporate this symmetry? Demanding locality for an action for metric gravity compatible with these principles determines the allowed operators, both for the purely gravitational part as well as matter couplings. The symmetries guarantee that there are two gravitational propagating physical degrees of freedom, but no explicit refoliation-invariance. The simplest such system has a geometric interpretation as a geodesic model in infinite-dimensional conformal superspace. One example of solution to the equations of motion corresponds to a static Bianchi IX spatial ansatz. The unique coupling to electromagnetism forces the electromagnetic equations to be hyperbolic, enabling us to “build” a standard space–time causal structure. There are, however, deviations from the standard Maxwell equations when space–time anisotropies become too large. Regarding quantization, with the geometric interpretation and the lack of refoliation invariance, the path integral treatment of the symmetries becomes much less involved than the similar approaches to GR. The symmetries form an (infinite-dimensional) Lie algebra, and no BFV treatment is necessary. Moreover, one can use gauge-invariant variational principles for selecting the boundary conditions of the path integral. We find that the propagator around the homogeneous solution has up to 6th order spatial derivatives, giving it plausible regularization properties as in Horava–Lifschitz.

• OSTI ID: 22848367
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 397; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
COMPUTERIZED SIMULATION
CONFORMAL INVARIANCE
DEGREES OF FREEDOM
ELECTROMAGNETISM
EQUATIONS OF MOTION
GAUGE INVARIANCE
GRAVITATION
LIE GROUPS
MAXWELL EQUATIONS
PROPAGATOR
QUANTIZATION
QUANTUM GRAVITY
STANDARDS
THREE-DIMENSIONAL CALCULATIONS