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A generalization of the Virasoro algebra to arbitrary dimensions. (English) Zbl 1229.81129
Summary: 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.

MSC:
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T10 Model quantum field theories
82B27 Critical phenomena in equilibrium statistical mechanics
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