Gravity as BF theory plus potential

Abstract

Spin foam models of quantum gravity are based on Plebanski's formulation of general relativity as a constrained BF theory. We give an alternative formulation of gravity as BF theory plus a certain potential term for the B-field. When the potential is taken to be infinitely steep one recovers general relativity. For a generic potential the theory still describes gravity in that it propagates just two graviton polarizations. The arising class of theories is of the type amenable to spin foam quantization methods, and, we argue, may allow one to come to terms with renormalization in the spin foam context.

7 pages, published in Proceedings of the Second Workshop on Quantum Gravity and Noncommutative Geometry (Lisbon, Portugal)

References in corpus (6)

• A New Spin Foam Model for 4d Gravity
• On deformations of Ashtekar's constraint algebra
• Renormalizable Non-Metric Quantum Gravity?
• Plebanski gravity without the simplicity constraints
• Note on non-metric gravity
• Motion of a "small body" in non-metric gravity

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• Effective Spin Foam Models for Four-Dimensional Quantum Gravity
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• From spin foams to area metric dynamics to gravitons
• Towards effective actions for the continuum limit of spin foams
• New action for simplicial gravity in four dimensions
• Consistent matter couplings for Plebanski gravity
• Twisted geometries are area-metric geometries
• Pure Connection Formulation, Twistors and the Chase for a Twistor Action for General Relativity
• Area-metric gravity revisited
• The new spin foam models and quantum gravity
• Four-Dimensional Entropy from Three-Dimensional Gravity
• Deformations of GR, Geometrodynamics and Reality Conditions
• Field redefinitions and Plebanski formalism for GR
• Canonical structure of minimal varying $\Lambda$ theories
• Aspects of Gravitational Wave/Particle Duality: Bulk Torsion $\leftrightarrow$ Boundary Gravity Correspondence
• Perspectives of Perihelion Precession in Torsion Modified Gravity