A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity

Abstract

Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any choice of spacetime dimension and signature, whose Feynman amplitudes are given by path integrals for clearly identified discrete gravity actions, in 1st order variables. In the 3-dimensional case, the corresponding discrete action is that of 1st order Regge calculus for gravity (generalized to include higher order corrections), while in higher dimensions, they correspond to a discrete BF theory (again, generalized to higher order) with an imposed orientation restriction on hinge volumes, similar to that characterizing discrete gravity. The new models shed also light on the large distance or semi-classical approximation of spin foam models. This new class of group field theories may represent a concrete unifying framework for loop quantum gravity and simplicial quantum gravity approaches.

arXiv comment48 pages, 4 figures, RevTeX, one reference added

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Cited by in corpus (17)

• Loop Quantum Cosmology: A Status Report
• The Tensor Track, III
• Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
• Casting Loop Quantum Cosmology in the Spin Foam Paradigm
• Loop Quantum Cosmology and Spin Foams
• Simplicity and closure constraints in spin foam models of gravity
• Critical Overview of Loops and Foams
• Random Tensors and Quantum Gravity
• Pushing Further the Asymptotics of the 6j-symbol
• Diffeomorphism symmetry in quantum gravity models
• Group field theory and simplicial quantum gravity
• Encoding simplicial quantum geometry in group field theories
• Wilson loops, geometric operators and fermions in 3d group field theory
• Emergent matter from 3d generalised group field theories
• Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity
• A Kirchhoff-like conservation law in Regge calculus
• Hilbert space formalisms for group field theory