Exact results for three- and four-point ladder diagrams with an arbitrary number of rungs

An Approach to the evaluation of three and four point ladder diagrams

We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries. Time-reversal symmetry in the boundary theory means that unorientable spacetimes must be considered in the bulk. In such a case, the partition function of JT gravity is still related to the volume of the moduli space of conformal structures, but this volume has a quantum correction and has to be computed using Reidemeister-Ray-Singer "torsion." Presence of fermions in the boundary theory (and thus a symmetry $(-1)^F$) means that the bulk has a spin or pin structure. Supersymmetry in the boundary means that the bulk theory is associated to JT supergravity and is related to the volume of the moduli space of super Riemann surfaces rather than of ordinary Riemann surfaces. In all cases we match JT gravity or supergravity with an appropriate random matrix ensemble. All ten standard random matrix ensembles make an appearance -- the three Dyson ensembles and the seven Altland-Zirnbauer ensembles. To facilitate the analysis, we extend to the other ensembles techniques that are most familiar in the case of the original Wigner-Dyson ensemble of hermitian matrices. We also generalize Mirzakhani's recursion for the volumes of ordinary moduli space to the case of super Riemann surfaces.

JT Gravity and the Ensembles of Random Matrix Theory

This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, web sites, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation.

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Bibliographic guide to the foundations of quantum mechanics and quantum information

Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and separation of variables

A scalar ladder propagator-type diagram is rigorously calculated in an arbitrary order of perturbation theory.

Calculation of ladder diagrams in arbitrary order

Exact solution of the Schwarzian theory

We propose a method of evaluating path integrals such that the integral is approximated with any accuracy by summations of a finite number of terms of an absolutely convergent series.

Method of approximate evaluation of path integrals using perturbation theory with convergent series. I

A regular approach to evaluate the functional integrals over the quasi-invariant measure on the group of diffeomorphisms is presented. As an important example of the application of this technique, we explicitly evaluate the correlation functions in the Schwarzian theory.

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Correlation functions in the Schwarzian theory

The proof is given of the method suggested in the previous paper for an approximate evaluation of path integrals in Hilbert space where the Gaussian measure is defined by a kernel operator.

Vladimir V. Belokurov

Papers

Calculation of ladder diagrams in arbitrary order

Exact solution of the Schwarzian theory

Method of approximate evaluation of path integrals using perturbation theory with convergent series. I

Correlation functions in the Schwarzian theory

Method for approximate evaluation of path integrals using perturbation theory with convergent series. II. Euclidean quantum field theory