Multi-orientable Group Field Theory

Abstract

Group Field Theories (GFT) are quantum field theories over group manifolds; they can be seen as a generalization of matrix models. GFT Feynman graphs are tensor graphs generalizing ribbon graphs (or combinatorial maps); these graphs are dual not only to manifolds. In order to simplify the topological structure of these various singularities, colored GFT was recently introduced and intensively studied since. We propose here a different simplification of GFT, which we call multi-orientable GFT. We study the relation between multi-orientable GFT Feynman graphs and colorable graphs. We prove that tadfaces and some generalized tadpoles are absent. Some Feynman amplitude computations are performed. A few remarks on the renormalizability of both multi-orientable and colorable GFT are made. A generalization from three-dimensional to four-dimensional theories is also proposed.

20 pages, 15 figures; v2: more details on the motivation for introducing this class of GFTs have been given; section 2 ("Multi-orientable GFT in three dimensions") has been slightly shortened; several references have been added

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• The 1/N expansion of colored tensor models
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• Scaling behaviour of three-dimensional group field theory
• Diffeomorphisms in group field theories
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• Renormalization of the Orientable Non-commutative Gross-Neveu Model
• Generalization of the Bollobás-Riordan polynomial for tensor graphs
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• Spectra of Operators in Large $N$ Tensor Models
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• Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Phases Of Melonic Quantum Mechanics
• Cut and join operator ring in Aristotelian tensor model
• Combinatorial study of graphs arising from the Sachdev-Ye-Kitaev model
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• Super-Group Field Cosmology
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• From Kronecker to tableau pseudo-characters in tensor models
• Majorana Fermion Quantum Mechanics for Higher Rank Tensors
• Conformality of $1/N$ corrections in SYK-like models
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• Tensor and Matrix models: a one-night stand or a lifetime romance?
• Melonic Dominance in Subchromatic Sextic Tensor Models
• Nilpotent Symmetries in Super-Group Field Cosmology
• Polchinski's exact renormalisation group for tensorial theories: Gaussian universality and power counting
• A canonical rank-three tensor model with a scaling constraint
• Spectrum of a Gross-Neveu Yukawa model with flavor disorder in $d=3$
• Hagedorn Temperature in Large $N$ Majorana Quantum Mechanics
• Melonic Turbulence
• Fourth Quantization
• Surgery in colored tensor models
• Renormalization and Hopf Algebraic Structure of the 5-Dimensional Quartic Tensor Field Theory
• Diagrammatics of the quartic $O(N{)}^3$-invariant Sachdev-Ye-Kitaev-like tensor model
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• Super-group field cosmology in Batalin-Vilkovisky formulation
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• Renormalizability of Supersymmetric Group Field Cosmology
• Duality of O(N) and Sp(N) random tensor models: tensors with symmetries