HHL correlators, orbit averaging and form factors

Abstract

We argue that the conventional method to calculate the OPE coefficients in the strong coupling limit for heavy-heavy-light operators in the N=4 Super-Yang-Mills theory has to be modified by integrating the light vertex operator not only over a single string worldsheet but also over the moduli space of classical solutions corresponding to the heavy states. This reflects the fact that we are primarily interested in energy eigenstates and not coherent states. We tested our prescription for the BMN vacuum correlator, for folded strings on $S^5$ and for two-particle states. Our prescription for two-particle states with the dilaton leads to a volume dependence which matches exactly to the structure of finite volume diagonal formfactors. As the volume depence does not rely on the particular light operator we conjecture that symmetric OPE coefficients can be described for any coupling by finite volume diagonal form factors.

32 pages, 1 figure; v2: small corrections including signs, references added

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• Diagonal finite volume matrix elements in the sinh-Gordon model
• Exact finite volume expectation values of local operators in excited states
• From Spin Vertex to String Vertex
• Entanglement and mixed states of Young tableau states in gauge/gravity correspondence