A String Bit Hamiltonian Approach to Two-Dimensional Quantum Gravity

TL;DR

This paper introduces solvable string bit Hamiltonian models for two-dimensional quantum gravity, connecting them to known transfer matrix models and expanding the theoretical framework of quantum gravity in lower dimensions.

Contribution

It presents a new class of solvable Hamiltonian models based on string bits and the Virasoro algebra, linking them to existing quantum gravity models.

Findings

Models are solvable and exactly analyzable.

Scaling limits match known 2D quantum gravity transfer matrix models.

Provides a new algebraic framework for quantum gravity in two dimensions.

Abstract

Motivated by the formalism of string bit models, or quantum matrix models, we study a class of simple Hamiltonian models of quantum gravity type in two space-time dimensions. These string bit models are special cases of a more abstract class of models defined in terms of the sl(2) subalgebra of the Virasoro algebra. They turn out to be solvable and their scaling limit coincides in special cases with known transfer matrix models of two-dimensional quantum gravity.