A simple proof of orientability in colored group field theory

Abstract

In this short note we use results from the theory of crystallizations to prove that color in group field theories garantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. The origin of orientability is the presence of two interaction vertices.

5 pages two columns, 3 figures; presentation improved, title changed

References in corpus (6)

• Group field theory renormalization - the 3d case: power counting of divergences
• Topological Graph Polynomials in Colored Group Field Theory
• Bosonic Colored Group Field Theory
• Scaling behaviour of three-dimensional group field theory
• Linearized Group Field Theory and Power Counting Theorems
• The group field theory approach to quantum gravity: some recent results

Cited by in corpus (8)

• Colored Tensor Models - a Review
• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• The Complete Barrett-Crane Model and its Causal Structure
• Extending the Tutte and Bollobás-Riordan Polynomials to Rank 3 Weakly-Colored Stranded Graphs
• GEMs and amplitude bounds in the colored Boulatov model
• Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model