Melonic phase transition in group field theory

Baratin, A.; Carrozza, S.; Oriti, D.; Ryan, James; Smerlak, M.

doi:10.1007/s11005-014-0699-9

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学術論文

Melonic phase transition in group field theory

MPS-Authors

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Baratin, A.
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Carrozza, S.
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Oriti, D.
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Ryan, James
Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Smerlak, M.
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1307.5026.pdf
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art%3A10.1007%2Fs11005-014-0699-9.pdf
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引用

Baratin, A., Carrozza, S., Oriti, D., Ryan, J., & Smerlak, M. (2014). Melonic phase transition in group field theory. Letters in Mathematical Physics, 104(8), 1003-1017. doi:10.1007/s11005-014-0699-9.

引用: https://hdl.handle.net/11858/00-001M-0000-0024-24A8-9

要旨

Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of four dimensional models of quantum gravity.