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Holographic variables for CFT$_2$ conformal blocks with heavy operators | | K.B.Alkalaev
; Mikhail Pavlov
; | | Date: |
8 Jan 2020 | | Abstract: | We consider large-$c$ $n$-point Virasoro blocks with $n-k$ background heavy
operators and $k$ perturbative heavy operators. Conformal dimensions of heavy
operators scale linearly with large $c$, while splitting into
background/perturbative operators assumes an additional perturbative expansion.
Such conformal blocks can be calculated within the monodromy method that
basically reduces to solving auxiliary Fuchsian second-order equation and
finding monodromy of solutions. We show that there exist particular variables
that we call holographic, use of which drastically simplifies the whole
analysis. In consequence, we formulate the uniformization property of the
large-$c$ blocks which states that in the holographic variables their form
depends only on the number of perturbative heavy operators. On the other hand,
the holographic variables encode the metric in the bulk space so that the
conformal blocks with the same number of perturbative operators are calculated
by the same geodesic trees but on different geometries created by the
background operators. | | Source: | arXiv, 2001.2604 | | Services: | Forum | Review | PDF | Favorites | |
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