Large-$c$ conformal $(n \leq 6)$-point blocks with superlight weights and holographic Steiner trees

TL;DR

This paper investigates large central charge conformal blocks in 2D CFTs with heavy operators, calculating holographic Steiner tree lengths in the superlight approximation, extending to higher points and generalizations.

Contribution

It introduces a method to compute holographic Steiner tree lengths for multi-point conformal blocks with superlight weights in the large-$c$ limit.

Findings

Derived lengths of Steiner trees for 5- and 6-point blocks.

Generalized results for N-point conformal blocks.

Extended superlight approximation to higher-point cases.

Abstract

In this note we study CFT$_2$ Virasoro conformal blocks with heavy operators in the large-$c$ limit in the context of AdS$_3$/CFT$_2$ correspondence. We compute the lengths of the holographic Steiner trees dual to the $5$-point and $6$-point conformal blocks using the superlight approximation when one or more dimensions are much less than the others. These results are generalized for $N$-point holographic Steiner trees dual to $(N+1)$-point conformal blocks with superlight weights.