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3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory

Winston Fairbairn·Etera R. Livine
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Abstract

An effective field theory for matter coupled to three-dimensional quantum gravity was recently derived in the context of spinfoam models in hep-th/0512113. In this paper, we show how this relates to group field theories and generalized matrix models. In the first part, we realize that the effective field theory can be recasted as a matrix model where couplings between matrices of different sizes can occur. In a second part, we provide a family of classical solutions to the three-dimensional group field theory. By studying perturbations around these solutions, we generate the dynamics of the effective field theory. We identify a particular case which leads to the action of hep-th/0512113 for a massive field living in a flat non-commutative space-time. The most general solutions lead to field theories with non-linear redefinitions of the momentum which we propose to interpret as living on curved space-times. We conclude by discussing the possible extension to four-dimensional spinfoam models.

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Winston Fairbairn, Etera R. Livine. 2007-02-23. 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory. https://doi.org/10.1088/0264-9381%2F24%2F20%2F021

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