Abstract
We consider structure constants of single-trace operators at strong coupling in planar mathcal{N} = 4 SYM theory using the hexagon formalism. We concentrate on heavy-heavy- light correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator. They describe the couplings between two highly boosted strings and a supergravity mode in the bulk dual. In the hexagon framework, two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor. The former originates from giant mirror magnons scanning the AdS geometry while the latter stems from small fluctuations around the BMN vacuum. The resulting structure constants have poles at positions where an enhanced mixing with double-trace operators is expected and zeros whenever the process is forbidden by supersymmetry. We also discuss the transition to the classical regime, when the length of the light operator scales like the string tension, where we observe similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex.
Highlights
Correction to the 4pt functions of single-trace chiral primary operators of arbitrary dimensions ∼ g0, which generalises earlier results and proposals, see [11] and references therein
We concentrate on heavy-heavylight correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator
Two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor
Summary
In this paper we consider planar 3pt functions between two BPS operators and one nonBPS operator using the hexagon formalism. For application to structure constants with two half-BPS operators we can fold the wave functions as only the diagonal states with {yi} = {yi} return a non-zero answer. This superselection rule was derived in [55] from the diagonal rminP SU (2|2) Yangian symmetry of the hexagon form factors. It extends the global selection rule N = Nwhich states that only left-right symmetric representations show up in the OPE of two chiral primary operators.
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