Abstract
Recently we conjectured the four-point amplitude of graviton multiplets in AdS5 × S5 at one loop by exploiting the operator product expansion of mathcal{N} = 4 super Yang-Mills theory. Here we give the first extension of those results to include Kaluza-Klein modes, obtaining the amplitude for two graviton multiplets and two states of the first KK mode. Our method again relies on resolving the large N degeneracy among a family of long double-trace operators, for which we obtain explicit formulas for the leading anomalous dimensions. Having constructed the one-loop amplitude we are able to obtain a formula for the one-loop corrections to the anomalous dimensions of all twist five double-trace operators.
Highlights
Bootstrap the one-loop correction to the AdS5 scattering of four-graviton multiplets, or equivalently the 1/N 4 correction to the four-point correlator of four energy-momentum multiplets in the large N limit
Having constructed the one-loop amplitude we are able to obtain a formula for the one-loop corrections to the anomalous dimensions of all twist five double-trace operators
A crucial ingredient in the analysis is the resolution of a large degeneracy among the spectrum of double-trace operators which occurs in the strict large N limit
Summary
The basic objects we wish to consider are the single-trace half-BPS operators given by. Let us consider the correlators O2O2O3O3 and O2O3O2O3 , corresponding to AdS amplitudes of two graviton multiplets and two Kaluza-Klein modes. We write each correlation function as sum of its free theory contribution and an interacting term, O2O3O2O3 = O2O3O2O3 free + O2O3O2O3 int , O2O2O3O3 = O2O2O3O3 free + O2O2O3O3 int. The free theory correlation function has exactly two terms which we express as follows, O2O2O3O3 free = A O2O3O2O3 free = A. has been extracted so that the remaining factor is finite in the large N limit. The interacting parts, or equivalently the functions F (u, v) and G(u, v), have expansions of the form. In terms of the decomposition (2.5) the order a terms are special, in that they receive contributions from both free theory and from the interacting part of the correlator. In particular from OPE considerations we expect that the leading discontinuity at order an is of the form logn u
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