Abstract
We bootstrap loop corrections to AdS5 supergravity amplitudes by enforcing the consistency of the known classical results with the operator product expansion of mathcal{N} = 4 super Yang-Mills theory. In particular this yields much new information on the spectrum of double-trace operators which can then be used, in combination with superconformal symmetry and crossing symmetry, to obtain a prediction for the one-loop amplitude for four graviton multiplets in AdS. This in turn yields further new results on subleading O(1/N4) corrections to certain double-trace anomalous dimensions.
Highlights
Can extract from it information about non-protected operators, and it has been the object of a huge amount of research throughout the intervening time, both perturbatively [6,7,8,9,10,11,12,13,14,15,16]
Since the operators Op are protected by supersymmetry, their two-point functions and three-point functions are fully described by their free field expressions
The fact that the operators Op are half-BPS means that the four-point functions of any operators in the supermultiplets are uniquely determined in terms of the four-point functions of the superconformal primaries, p1p2p3p4 = Op1 (x1, y1)Op2 (x2, y2)Op3 (x3, y3)Op4 (x4, y4)
Summary
Since the operators Op are protected by supersymmetry, their two-point functions and three-point functions are fully described by their free field expressions. In other words their scaling dimensions and OPE coefficients are unrenormalised and independent of the Yang-Mills coupling. The fact that the operators Op are half-BPS means that the four-point functions of any operators in the supermultiplets are uniquely determined in terms of the four-point functions of the superconformal primaries, p1p2p3p4 = Op1 (x1, y1)Op2 (x2, y2)Op3 (x3, y3)Op4 (x4, y4). In free field theory the correlation functions can be written as polynomials in the superpropagators gij yi2j x2ij (2.3). To express the constraints imposed by superconformal symmetry it is useful to separate the correlator into a free-field piece and an interacting piece. The different N dependence of the two pieces comes from the fact that the first term in (2.10) corresponds to the disconnected part of the correlator while the second term is the connected part
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