The n-point functions of any Conformal Field Theory (CFT) in $d$ dimensions
can always be interpreted as spatial restrictions of corresponding functions in
a higher-dimensional CFT with dimension $d’> d$. In particular, when a
four-point function in $d$ dimensions has a known conformal block expansion,
this expansion can be easily extended to $d’=d+2$ due to a remarkable identity
among conformal blocks, discovered by Kaviraj, Rychkov, and Trevisani (KRT) as
a consequence of Parisi-Sourlas supersymmetry and confirmed to hold in any CFT
with $d > 1$. In this note, we provide an elementary proof of this identity
using simple algebraic properties of the Casimir operators. Additionally, we
construct five differential operators, $\Lambda_i$, which promote a conformal
block in $d$ dimensions to five conformal blocks in $d+2$ dimensions. These
operators can be normalized such that $\sum_i \Lambda_i = 1$, from which the
KRT identity immediately follows. Similar, simpler identities have been
proposed, all of which can be reformulated in the same way.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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