Abstract
We explore the structure of maximally supersymmetric Yang-Mills correlators in the supergravity regime. We develop an algorithm to construct one-loop supergravity amplitudes of four arbitrary Kaluza-Klein supergravity states, properly dualised into single- particle operators. We illustrate this algorithm by constructing new explicit results for multi-channel correlation functions, and we show that correlators which are degenerate at tree level become distinguishable at one-loop. The algorithm contains a number of subtle features which have not appeared until now. In particular, we address the presence of non- trivial low twist protected operators in the OPE that are crucial for obtaining the correct one-loop results. Finally, we outline how the differential operators D̂pqrs and ∆(8), which play a role in the context of the hidden 10d conformal symmetry at tree level, can be used to reorganise our one-loop correlators.
Highlights
Introduction and summaryRecently there has been significant progress in probing the structure of quantum gravity in the context of the AdS/CFT correspondence
We illustrate this algorithm by constructing new explicit results for multi-channel correlation functions, and we show that correlators which are degenerate at tree level become distinguishable at one-loop
We outline how the differential operators Dpqrs and ∆(8), which play a role in the context of the hidden 10d conformal symmetry at tree level, can be used to reorganise our one-loop correlators
Summary
There has been significant progress in probing the structure of quantum gravity in the context of the AdS/CFT correspondence. It is a generalisation of the tree-level function of Rastelli and Zhou for all N , and it is defined by the property that, together with connected free theory, it gives empty contributions to any exchanged long operators with twist 2 + 2a + b ≤ τ < τ min. There is no such a simplification in general, and the study of four point correlators with arbitrary external charges, which is the main subject of this paper, requires non trivially both Hp(2) and a novel Tp. let us point out a very remarkable feature of Hp(2): the three-point couplings Cp1p2,τ of exchanged semishort operators, which constrain a piece of G2,0, are obtained only within free theory, since these are not renormalized.
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