The large $N_c$ limit of four-point functions in N=4 super-Yang-Mills theory from anti-de Sitter Supergravity

TL;DR

This paper calculates the imaginary parts of four-point functions in N=4 super Yang-Mills theory using AdS/CFT, revealing simplified expressions that suggest hidden symmetries at large N_c and strong coupling.

Contribution

It provides explicit expressions for the imaginary parts of scalar four-point functions in AdS/CFT, including exchange diagrams, highlighting potential new symmetry structures.

Findings

Imaginary parts factorize into lower-point functions due to unitarity.

Results contain rational functions and logarithms, not free-field.

Suggests additional symmetry structures in the theory.

Abstract

We compute the imaginary part of scalar four-point functions in the AdS/CFT correspondence relevant to N=4 super Yang-Mills theory. Unitarity of the AdS supergravity demands that the imaginary parts of the correlation functions factorize into products of lower-point functions. We include the exchange diagrams for scalars as well as gravitons and find explicit expressions for the imaginary parts of these correlators. In momentum space these expressions contain only rational functions and logarithms of the kinematic invariants, in such a manner that the correlator is not a free-field result. The simplicity of these results, however, indicate the possibility of additional symmetry structures in N=4 super Yang-Mills theory in the large $N_c$ limit at strong effective coupling. The complete expressions may be computed from the integral results derived here.