Sine-square deformation and Mobius quantization of two-dimensional conformal field theory

TL;DR

This paper introduces a Mobius quantization method for 2D conformal field theory, connecting radial and dipolar quantizations, and reveals how the Virasoro algebra emerges as a continuum limit in this framework.

Contribution

It presents a novel Mobius quantization approach that unifies different quantization schemes in 2D CFT and elucidates the algebraic structure in the SSD limit.

Findings

Virasoro algebra in dipolar quantization is a continuum limit of scaled generators in SSD.

Mobius quantization bridges radial and dipolar quantizations in 2D CFT.

The approach provides insights into the algebraic structure of quantum critical systems.

Abstract

Motivated by sine-square deformation (SSD) for quantum critical systems in 1+1-dimension, we discuss a Mobius quantization approach to the two-dimensional conformal field theory (CFT), which bridges the conventional radial quantization and the dipolar quantization recently proposed by Ishibashi and Tada. We then find that the continuous Virasoro algebra of the dipolar quantization can be interpreted as a continuum limit of the Virasoro algebra for scaled generators in the SSD limit of the Mobius quantization approach.