The full Ward Takahashi Identity for arbitrary coloured tensor models: Focus on 3D and 4D quartic interactions

par Carlos Perez-Sanchez (Universität Münster)

vendredi 3 févr. 2017, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (Institut Camille Jordan)

Having a common backbone with matrix models, coloured tensor models is a random geometry approach to quantum gravity in arbitrary dimensions. In particular, regularly edge-coloured bipartite graphs—precisely the Feynman graphs of these theories—generalise ribbon graphs and represent orientable PL- manifolds of dimension one less than the number of colours. Also, an integer called Gurau’s degree, which generalises the genus, controls the 1/N expansion. We introduce a graph theoretical representation of the connected sum that is additive with respect to Gurau’s degree and compatible with the QFT-structure. Moreover, we find the general exact non-perturbative Ward Takahashi Identities and then discuss particular (with so-called melonic, or dominant, interaction vertices) quartic 3D and 4D coloured tensor theories. Recursions for the correlation functions of these theories are obtained.