Abstract
In this article we explore the holographic duals of tensor models using collective field theory. We develop a description of the gauge invariant variables of the tensor model. This is then used to develop a collective field theory description of the dynamics. We consider matrix like subsectors that develop an extra holographic dimension. In contrast to this, we argue that melonic large $N$ limits do not develop an extra dimension. The finite $N$ physics of the model is also developed and non-perturbative effects in the $1/N$ expansion are exhibited.
Highlights
In the last 20 years genuinely new and fascinating insights into the large N expansion have been achieved
The expansion identifies the surface triangulated by the ribbon graph with a string world sheet [1]. This initial proposal has found beautiful confirmation in the duality between the large N expansion of N 1⁄4 4 super-Yang-Mills theory and the loop expansion of IIB string theory on asymptotically AdS5 × S5 spacetimes [2,3,4]. This connection goes by the name of holography, or the gauge theory/gravity duality and for any theory with adjoint valued variables, one expects a duality with a string theory
In this article our goal has been to explore the holography of tensor models using collective field theory
Summary
In the last 20 years genuinely new and fascinating insights into the large N expansion have been achieved. Its strongly coupled large N limit has been constructed exactly and used to demonstrate that the model saturates the chaos bound [12] These features strongly suggest that the model is holographically dual to a black hole. For multimatrix models it is hard to parametrize the loop space of gauge invariants in a useful way and this has proved to be a central obstacle to deriving collective field theory. Since there are suggestions that tensor models are richer than vector models, but perhaps simpler than matrix models, it is worth examining their collective description This is our main goal in this article. We explicitly demonstrate how collective field theory reproduces correlators in a model with interactions This physics recovers many features expected of matrix models.
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