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arXiv · 1111.5842

Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity

Aristide Baratin·Daniele Oriti
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Abstract

In a recent work, a dual formulation of group field theories as non-commutative quantum field theories has been proposed, providing an exact duality between spin foam models and non-commutative simplicial path integrals for constrained BF theories. In light of this new framework, we define a model for 4d gravity which includes the Immirzi parameter gamma. It reproduces the Barrett-Crane amplitudes when gamma goes to infinity, but differs from existing models otherwise; in particular it does not require any rationality condition for gamma. We formulate the amplitudes both as BF simplicial path integrals with explicit non-commutative B variables, and in spin foam form in terms of Wigner 15j-symbols. Finally, we briefly discuss the correlation between neighboring simplices, often argued to be a problematic feature, for example, in the Barrett-Crane model.

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Aristide Baratin, Daniele Oriti. 2011-11-24. Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity. https://doi.org/10.1103/physrevd.85.044003

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