A Hamiltonian Formalism for Topological Recursion

TL;DR

This paper introduces a Hamiltonian formalism that connects spectral curves with their quantization via topological recursion, applicable to various models including minimal, supersymmetric, and gauge theories.

Contribution

It develops a novel Hamiltonian framework that systematically associates spectral curves with their topological recursion quantization, extending to diverse physical models.

Findings

Hamiltonians constructed for minimal and continuum DT models

Extension to supersymmetric and gauge theories

Demonstrates quantization of spectral curves via topological recursion

Abstract

We propose a string field Hamiltonian formalism that associates a class of spectral curves and provides their quantization through the Chekhov-Eynard-Orantin topological recursion. As illustrative examples, we present Hamiltonians for the $(2,2m-1)$ minimal discrete and continuum dynamical triangulation (DT) models, the supersymmetric analogue of minimal continuum DT models, the Penner model, and 4D $\mathcal{N}=2$ $SU(2)$ gauge theories in the self-dual $\Omega$-background.