On the modular operator of mutli-component regions in chiral CFT

Understand

We introduce a new approach to find the Tomita-Takesaki modular flow for multi-component regions in general chiral conformal field theory.

• Our method is based on locality and analyticity of primary fields as well as the so-called Kubo-Martin-Schwinger (KMS) condition.
• These features can be used to transform the problem to a Riemann-Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian.
• Examples are considered.