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AdS$\times$S Mellin Bootstrap, Hidden 10d Symmetry and Five-point Kaluza-Klein Functions in $\mathcal{N}=4$ SYM

Bruno Fernandes, Vasco Goncalves, Zhongjie Huang, Yichao Tang, Joao Vilas Boas, Ellis Ye Yuan

Abstract

We propose an AdS$\times$S factorization formula at the level of the generating function for correlators with arbitrary Kaluza-Klein configurations, and implement it in the supergravity limit of $\mathcal{N}=4$ super Yang-Mills. By incorporating this mechanism into Mellin space bootstrap, together with an observed $Z_2$ symmetry under AdS$\ \leftrightarrow\ $S, we manage to simultaneously work out unified formulas both for all five-point half-BPS correlators and for all four-point correlators with one superdescendant. This AdS\times$S bootstrap method is directly applicable to generic multi-point computation at tree level.

AdS$\times$S Mellin Bootstrap, Hidden 10d Symmetry and Five-point Kaluza-Klein Functions in $\mathcal{N}=4$ SYM

Abstract

We propose an AdSS factorization formula at the level of the generating function for correlators with arbitrary Kaluza-Klein configurations, and implement it in the supergravity limit of super Yang-Mills. By incorporating this mechanism into Mellin space bootstrap, together with an observed symmetry under AdSS, we manage to simultaneously work out unified formulas both for all five-point half-BPS correlators and for all four-point correlators with one superdescendant. This AdS\times$S bootstrap method is directly applicable to generic multi-point computation at tree level.

Paper Structure

This paper contains 5 sections, 96 equations, 1 figure, 1 table.

Table of Contents

  1. The spinning AdS$\,\times\,$S amplitudes and factorization
  2. Drukker-Plefka twist in $\rm AdS\times S$ space
  3. The expression of $P^{(0,0)}(\gamma_{ij},n_{ij})$
  4. Superspace method
  5. Computation of R-factors

Figures (1)

  • Figure 1: The position of non-zero residues in the five-point amplitude ansatz.