Four-point correlators of BPS operators in N=4 SYM at order g^4

TL;DR

This paper investigates the structure of four-point correlators of 1/2-BPS operators in N=4 SYM at two loops, revealing how degeneracies present at one loop are lifted or preserved depending on operator weight, supporting the AdS/CFT correspondence.

Contribution

The authors explicitly compute two-loop four-point correlators of BPS operators in N=4 SYM using N=2 harmonic superspace, analyzing degeneracy lifting at higher orders.

Findings

Degeneracy at one loop is lifted for weights 3 and 4 at two loops.

Degeneracy persists for weights greater than 4 at two loops.

Results support the AdS/CFT duality conjecture.

Abstract

We study the large N degeneracy in the structure of the four-point amplitudes of 1/2-BPS operators of arbitrary weight k in perturbative N=4 SYM theory. At one loop (order g^2) this degeneracy manifests itself in a smaller number of independent conformal invariant functions describing the amplitude, compared to AdS_5 supergravity results. To study this phenomenon at the two-loop level (order g^4) we consider a particular N=2 hypermultiplet projection of the general N=4 amplitude. Using the formalism of N=2 harmonic superspace we then explicitly compute this four-point correlator at two loops and identify the corresponding conformal invariant functions. In the cases of 1/2-BPS operators of weight k=3 and k=4 the one-loop large N degeneracy is lifted by the two-loop corrections. However, for weight k > 4 the degeneracy is still there at the two-loop level. This behavior suggests that for a given weight k the degeneracy will be removed if perturbative corrections of sufficiently high order are taken into account. These results are in accord with the AdS/CFT duality conjecture.