A generalization of the Virasoro algebra to arbitrary dimensions

Understand

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.