Abstract
We consider the strong coupling limit of 4-point functions of heavy operators in mathcal{N} = 4 SYM dual to strings with no spin in AdS. We restrict our discussion for operators inserted on a line. The string computation factorizes into a state-dependent sphere part and a universal AdS contribution which depends only on the dimensions of the operators and the cross ratios. We use the integrability of the AdS string equations to compute the AdS part for operators of arbitrary conformal dimensions. The solution takes the form of TBA-like integral equations with the minimal AdS string-action computed by a corresponding free-energy-like functional. These TBA-like equations stem from a peculiar system of functional equations which we call a χ-system. In principle one could use the same method to solve for the AdS contribution in the N-point function. The discrete data that parameterizes these solutions enters through the analog of the chemical-potentials in the TBA-like equations. Finally, for operators dual to strings spinning in the same equator in S5 (i.e. BPS operators of the same type) the sphere part is simple to compute. In this case (which is generically neither extremal nor protected) our result allows the construction of the complete, strong coupling 4-point function.
Highlights
We use the integrability of the AdS string equations to compute the AdS part for operators of arbitrary conformal dimensions
One of the most interesting objects to study in an interacting quantum field theory is the four-point function
This allows the computation of leading strong coupling behavior of certain 4-point functions in N = 4 SYM, which is the main purpose of this paper
Summary
One of the most interesting objects to study in an interacting quantum field theory is the four-point function. In conformal field theories these are the first N -point functions whose spacetime dependence is not explicitly fixed by conformal symmetry The computation of this correlator is generally highly nontrivial and obtaining explicit expressions outside the perturbative regime is typically impossible. In particular the correspondence [1] maps the strong coupling limit of N = 4 SYM to a theory of classical strings moving in an AdS5×S5 background. This allows the computation of leading strong coupling behavior of certain 4-point functions in N = 4 SYM, which is the main purpose of this paper. While we have mostly focused on the 4-point computation, we note that the method used below could in principle be applied for the corresponding N -point computation
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