Feynman Diagrams of Generalized Matrix Models and the Associated Manifolds in Dimension 4

TL;DR

This paper explores how Feynman diagrams from tensor theories can be used to encode and reconstruct four-dimensional manifolds, contributing to quantum gravity research by linking combinatorial topology with quantum field theory.

Contribution

It demonstrates a method to associate combinatorial 4-manifolds with Feynman diagrams of specific tensor theories, advancing the mathematical understanding of quantum gravity models.

Findings

Feynman diagrams can encode 4-manifold structures

Tensor theories relate to combinatorial topology in 4D

Potential framework for quantum gravity models

Abstract

The problem of constructing a quantum theory of gravity has been tackled with very different strategies, most of which relying on the interplay between ideas from physics and from advanced mathematics. On the mathematical side, a central role is played by combinatorial topology, often used to recover the space-time manifold from the other structures involved. An extremely attractive possibility is that of encoding all possible space-times as specific Feynman diagrams of a suitable field theory. In this work we analyze how exactly one can associate combinatorial 4-manifolds to the Feynman diagrams of certain tensor theories.