The 1/N expansion of colored tensor models in arbitrary dimension

TL;DR

This paper generalizes the 1/N expansion to group field theories in any dimension, showing that at leading order only spherical graphs contribute, thus advancing understanding of tensor models in higher dimensions.

Contribution

It extends the 1/N expansion framework to arbitrary-dimensional group field theories and identifies the dominant spherical graphs in the large N limit.

Findings

Only spherical graphs contribute at leading order in large N limit.

The 1/N expansion is valid in arbitrary dimensions for group field theories.

Provides a foundation for analyzing higher-dimensional tensor models.

Abstract

In this paper we extend the 1/N expansion introduced in [1] to group field theories in arbitrary dimension and prove that only graphs corresponding to spheres S^D contribute to the leading order in the large N limit.