Virasoro algebras, kinematic space and the spectrum of modular Hamiltonians in CFT$_2$

TL;DR

This paper constructs eigenmodes of the vacuum modular Hamiltonian in 2D CFT, revealing their relation to the Virasoro algebra and suggesting a kinematic space framework for understanding the theory.

Contribution

It introduces an infinite class of eigenmodes with integer eigenvalues for the modular Hamiltonian in 2D CFT and links them to the Virasoro algebra on kinematic space.

Findings

Eigenmodes have integer eigenvalues and relate to the Virasoro algebra.

Eigenmodes act on OPE blocks and have bulk duals.

Results suggest a kinematic space description of 2D CFT.

Abstract

We construct an infinite class of eigenmodes with integer eigenvalues for the Vacuum Modular Hamiltonian of a single interval $N$ in 2d CFT and study some of its interesting properties, which includes its action on OPE blocks as well as its bulk duals. Our analysis suggests that these eigenmodes, like the OPE blocks have a natural description on the so called kinematic space of CFT$_2$ and in particular realize the Virasoro algebra of the theory on this kinematic space. Taken together, our results hints at the possibility of an effective description of the CFT$_2$ in the kinematic space language.