Large-N melonic tensor integrals are universal: they depend only on vertex counts, not on tensor rank D≥3 or the fine-grained combinatorics of the melonic invariants.
Quantum Gravity and Random Tensors
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abstract
Random tensors are the natural generalization of random matrices to higher order objects. They provide generating functions for random geometries and, assuming some familiarity with random matrix theory and quantum field theory, we discuss in the first part of this note the applications of such models to quantum gravity. In a second part we review tensor field theories, that is standard field theories in $\mathbb{R}^d$ but with tensor fields, which lead to a new family of large $N$ conformal field theories relevant for the study of the $AdS/CFT$ correspondence.
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Reviews basic definitions and properties of QFT vector models for induced quantum gravity and points out directions for future research.
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Twofold universality of large-$N$ melonic random tensors
Large-N melonic tensor integrals are universal: they depend only on vertex counts, not on tensor rank D≥3 or the fine-grained combinatorics of the melonic invariants.
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Induced quantum gravity from QFT vector models
Reviews basic definitions and properties of QFT vector models for induced quantum gravity and points out directions for future research.
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Quantum chaotic systems: a random-matrix approach
Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.