All Tree-Level Correlators for M Theory on AdS7×S4

Abstract

We present a constructive derivation of all four-point tree-level holographic correlators for eleven dimensional supergravity on AdS 7 × S 4. These correlators correspond to four-point functions of arbitrary one-half BPS operators in the six-dimensional (2,0) theory at large central charge. The crucial observation is that the polar part of the correlators in Mellin space is fully captured by a drastically simpler maximally R-symmetry violating amplitude, while the contact part is fully fixed by superconformal Ward identities and the flat space limit.

More on holographic correlators: twisted and dimensionally reduced structures

“…This led to several efficient new methods to compute holographic correlators, which avoid inputting the details of the complicated supergravity effective actions altogether. 1 Most spectacularly, the bootstrap methods gave a complete solution to all tree-level four-point functions of half-BPS operators for AdS 5 × S 5 IIB supergravity [9,10], without computing a single Witten diagram. On the other hand, the success of these methods in other maximally supersymmetric backgrounds (AdS 4 × S 7 and AdS 7 × S 4 ) was much more modest.…”

“…While many new results, unattainable by brute force, were generated by using these methods [11][12][13], the algebraic bootstrap problems were too difficult to solve in general. It was only recently that a different constructive method was developed [1,2] which completed the program for tree-level half-BPS four-point functions in maximally supersymmetric theories. The constructive method starts with a special Rsymmetry polarization configuration, dubbed "maximally R-symmetry violating" in [1,2], where correlators drastically simplify and can be easily computed.…”

“…It was only recently that a different constructive method was developed [1,2] which completed the program for tree-level half-BPS four-point functions in maximally supersymmetric theories. The constructive method starts with a special Rsymmetry polarization configuration, dubbed "maximally R-symmetry violating" in [1,2], where correlators drastically simplify and can be easily computed. The full correlators are then reconstructed from this limit by using symmetries.…”

“…The full correlators are then reconstructed from this limit by using symmetries. This method applies to any spacetime dimension, and leads to a closed form formula for all tree-level four-point functions in all maximally supersymmetric theories [1,2].…”

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Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1,2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties.

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