Multi-orientable group field theory

Abstract

Group field theories (GFTs) 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 not always dual to manifolds. In order to simplify the topological structure of these various singularities, colored GFT was recently introduced and intensively studied. 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.