A generalization of the Virasoro algebra to arbitrary dimensions

TL;DR

This paper extends the Virasoro algebra to higher dimensions using colored tensor models, deriving the algebra of constraints that govern their large N behavior and revealing a new Lie algebra structure indexed by trees.

Contribution

It introduces a generalized Virasoro algebra for arbitrary dimensions based on colored tensor models with generic interactions.

Findings

Constraints form a Lie algebra indexed by trees

Generalization of Virasoro algebra to higher dimensions

Large N limit analysis of tensor models

Abstract

Colored tensor models generalize matrix models in higher dimensions. They admit a 1/N expansion dominated by spherical topologies and exhibit a critical behavior strongly reminiscent of matrix models. In this paper we generalize the colored tensor models to colored models with generic interaction, derive the Schwinger Dyson equations in the large N limit and analyze the associated algebra of constraints satisfied at leading order by the partition function. We show that the constraints form a Lie algebra (indexed by trees) yielding a generalization of the Virasoro algebra in arbitrary dimensions.