Finite-N bootstrap yields N-independent bounds for matrix models but N-dependent novel bounds on the two-point function versus quartic coupling for tensor models.
Canonical reference
2D Gravity and Random Matrices
Canonical reference. 83% of citing Pith papers cite this work as background.
9
Pith papers citing it
Background
83% of classified citations
abstract
We review recent progress in 2D gravity coupled to $d<1$ conformal matter, based on a representation of discrete gravity in terms of random matrices. We discuss the saddle point approximation for these models, including a class of related $O(n)$ matrix models. For $d<1$ matter, the matrix problem can be completely solved in many cases by the introduction of suitable orthogonal polynomials. Alternatively, in the continuum limit the orthogonal polynomial method can be shown to be equivalent to the construction of representations of the canonical commutation relations in terms of differential operators. In the case of pure gravity or discrete Ising--like matter, the sum over topologies is reduced to the solution of non-linear differential equations (the Painlev\'e equation in the pure gravity case) which can be shown to follow from an action principle. In the case of pure gravity and more generally all unitary models, the perturbation theory is not Borel summable and therefore alone does not define a unique solution. In the non-Borel summable case, the matrix model does not define the sum over topologies beyond perturbation theory. We also review the computation of correlation functions directly in the continuum formulation of matter coupled to 2D gravity, and compare with the matrix model results. Finally, we review the relation between matrix models and topological gravity, and as well the relation to intersection theory of the moduli space of punctured Riemann surfaces.
citation-role summary
background 5
other 1
citation-polarity summary
representative citing papers
Two novel proofs establish equivalence between path integral and stochastic quantizations for scalar Euclidean QFTs via forest-indexed Taylor interpolations.
Collective excitations analogous to phonons are derived in quantum gravity condensates within a group field theory model, yielding leading beyond-mean-field corrections to emergent Friedmann dynamics.
Proposes complex matrix models for BPS correlators in N=4 SYM, relating eigenvalue distributions to LLM droplet shapes and enabling computations of one-point functions and three-point correlators via reductions to known models.
Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.
Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.
A review of the chaos-assisted holographic correspondence linking the SYK model to 2D JT gravity, including the need for string theory corrections at fine quantum scales.
Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.