Crossing-symmetric Twist Field Correlators and Entanglement Negativity in Minimal CFTs

TL;DR

This paper develops a new formalism for calculating twist field correlators in minimal conformal field theories, with applications to entanglement measures and bounds on structure constants, using covering map techniques and conformal block expansions.

Contribution

It introduces a convergent expansion of twist field correlators in minimal CFTs and applies it to entanglement and bootstrap bounds, advancing computational methods in the field.

Findings

Derived a fast convergent expansion for twist correlators

Applied the formalism to entanglement of disjoint intervals

Refined bounds on structure constants in unitary CFTs

Abstract

We study conformal twist field four-point functions on a $\mathbb Z_N$ orbifold. We examine in detail the case $N=3$ and analyze theories obtained by replicated $N$-times a minimal model with central charge $c<1$. A fastly convergent expansion of the twist field correlation function in terms of sphere conformal blocks with central charge $Nc$ is obtained by exploiting covering map techniques. We discuss extensive applications of the formalism to the entanglement of two disjoint intervals in CFT, in particular we propose a conformal block expansion for the partially transposed reduced density matrix. Finally, we refine the bounds on the structure constants of unitary CFTs determined previously by the genus two modular bootstrap.