Matrix-Tensor Models and Melonic Feynman Graphs

Abstract

Matrix-tensor models give rise to a special type of Feynman graphs: the melonic graphs. These graphs can all be obtained by repeatedly inserting a melon, which is a certain fundamental building block, onto propagators in the graph. Matrix-tensor models are connected to the quantum mechanical description of black holes.

In this thesis, we first introduce matrix-tensor models and their properties. Then, we present a new set of interaction terms - the so-called MST interactions on a complete graph - and prove that all the associated Feynman graphs are melonic.

Also, we introduce a new limiting procedure that in certain cases selects not only the melonic graphs, but also graphs that can be embedded into surfaces of higher genus. Finally, we discuss two combinatorial approaches to computing the two-point function in theories with melonic graphs.