Lecturer: Dr. Shota Komatsu
Affiliation: Perimeter Institute for Theoretical Physics
Abstract:
We propose a nonperturbative framework
to study general correlation functions of
single-trace operators in N = 4 SYM at
large N. The basic strategy is to
decompose them into fundamental
building blocks called the hexagon form
factors, which were introduced earlier to
study structure constants using
integrability. The decomposition is akin to
a triangulation of a Riemann surface, and
we thus call it hexagonalization. We
propose a set of rules to glue the
hexagons together based on symmetry,
which naturally incorporate the
dependence on the conformal and the R-
symmetry cross ratios. Our method is
conceptually different from the
conventional operator product expansion
and automatically takes into account
multi-trace operators exchanged in OPE
channels. To illustrate the idea in simple
set-ups, we compute four-point functions
of BPS operators of arbitrary lengths and
correlation functions of one Konishi
operator and three short BPS operators,
all at one loop. In all cases, the results are
in perfect agreement with the perturbative
data. We also suggest that our method
can be a useful tool to study conformal
integrals, and show it explicitly for the
case of ladder integrals.
Additional details of the upcoming Joint
Seminars in Theoretical High Energy Physics
can be found on the following link.