Wilson loops, geometric operators and fermions in 3d group field theory

Abstract

Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin network grasping operators which require the introduction of vector fields on the group. We then use this to define group field theories that give a previously defined spin foam model for fermion fields coupled to gravity, and the simpler quenched approximation, by using tensor fields on the group. The group field theory naturally includes the sum over fermionic loops at each order of the perturbation theory.

13 pages, many figures, uses psfrag

References in corpus (6)

• 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
• Ponzano-Regge model revisited II: Equivalence with Chern-Simons
• Fermions in three-dimensional spinfoam quantum gravity
• A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
• Extended matter coupled to BF theory
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Cited by in corpus (7)

• Homogeneous cosmologies as group field theory condensates
• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
• Group field theory for quantum gravity minimally coupled to a scalar field
• Loop quantum cosmology from group field theory
• Observables in 3d spinfoam quantum gravity with fermions
• Emergent matter from 3d generalised group field theories
• From Dimensional Reduction of 4d Spin Foam Model to Adding Non-Gravitational Fields to 3d Spin Foam Model