Time development of conformal field theories associated with $L_{1}$ and $L_{-1}$ operators

TL;DR

This paper explores how unconventional time evolution in 2D conformal field theories, influenced by specific operators, affects algebraic structures and entanglement entropy, revealing the necessity of a cut-off near fixed points.

Contribution

It demonstrates that maintaining the Virasoro algebra under such evolution requires a cut-off, which naturally allows for the derivation of entanglement entropy formulas.

Findings

Virasoro algebra retention needs a cut-off near fixed points

Introduction of a scale enables natural derivation of entanglement entropy

Unconventional time development impacts algebraic and entropic properties

Abstract

In this study, we examined consequences of unconventional time development of two-dimensional conformal field theory induced by the $L_{1}$ and $L_{-1}$ operators, employing the formalism previously developed in a study of sine-square deformation. We discovered that the retainment of the Virasoro algebra requires the presence of a cut-off near the fixed points. The introduction of a scale by the cut-off makes it possible to recapture the formula for entanglement entropy in a natural and straightforward manner.