Infinite circumference limit of conformal field theory

TL;DR

This paper explores an infinite circumference limit in 2D conformal field theory by redefining the Hamiltonian, revealing a continuous spectrum and algebra, inspired by sine-square deformation phenomena.

Contribution

It introduces a novel Hamiltonian choice in CFT that leads to an infinite circumference limit, connecting to sine-square deformation effects.

Findings

The theory exhibits a continuous and heavily degenerated spectrum.

The Virasoro algebra becomes continuous in this limit.

The approach explains peculiar behaviors in sine-square deformed systems.

Abstract

We argue that an infinite circumference limit can be obtained in 2-dimensional conformal field theory by adopting $L_0-(L_1+L_{-1})/2$ as a Hamiltonian instead of $L_0$. The theory obtained has a circumference of infinite length and hence exhibits a continuous and heavily degenerated spectrum as well as the continuous Virasoro algebra. The choice of this Hamiltonian was inspired partly by the so-called sine-square deformation, which is found in the study of a certain class of quantum statistical systems. The enigmatic behavior of sine-square deformed systems such as the sharing of their vacuum states with the closed boundary systems can be understood by the appearance of an infinite circumference.