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

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.