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

39 pages, 5 figures, 2 tables. Typos corrected. Final version published in JHEP

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