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Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling

Vasco Gonçalves

TL;DR

This work computes the first stringy corrections to the four-point function of the N=4 stress-tensor multiplet at strong coupling using Mellin amplitudes and the flat space limit, constrained by OPE data and supersymmetric relations to the Lagrangian correlator. The authors derive a structured 1/\lambda expansion for the Mellin amplitude, identify how corrections are polynomials in the Mellin variables, and extract explicit corrections to the anomalous dimensions of double-trace operators as well as predictions for higher-twist unprotected exchanges. They also translate these results into physical observables, obtaining the leading and first subleading corrections to energy-energy correlators (event shapes) and confirming consistency with known strong-coupling limits and Ward identities, aided by a Borel-resummed treatment of the series. Overall, the paper demonstrates that flat-space constraints, Mellin-space techniques, and supersymmetry together tightly constrain stringy corrections in AdS/CFT, with concrete predictions for CFT data and energy-flow observables at strong coupling.

Abstract

In this short note we use the flat space limit and the relation between the 4-pt correlation function of the bottom and top components of the stress tensor multiplet to constraint its stringy corrections at strong coupling in the planar limit. Then we use this four point function to compute corrections to the anomalous dimension of double trace operators of the Lagrangian density and to compute energy-energy correlators at strong coupling.

Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling

TL;DR

This work computes the first stringy corrections to the four-point function of the N=4 stress-tensor multiplet at strong coupling using Mellin amplitudes and the flat space limit, constrained by OPE data and supersymmetric relations to the Lagrangian correlator. The authors derive a structured 1/\lambda expansion for the Mellin amplitude, identify how corrections are polynomials in the Mellin variables, and extract explicit corrections to the anomalous dimensions of double-trace operators as well as predictions for higher-twist unprotected exchanges. They also translate these results into physical observables, obtaining the leading and first subleading corrections to energy-energy correlators (event shapes) and confirming consistency with known strong-coupling limits and Ward identities, aided by a Borel-resummed treatment of the series. Overall, the paper demonstrates that flat-space constraints, Mellin-space techniques, and supersymmetry together tightly constrain stringy corrections in AdS/CFT, with concrete predictions for CFT data and energy-flow observables at strong coupling.

Abstract

In this short note we use the flat space limit and the relation between the 4-pt correlation function of the bottom and top components of the stress tensor multiplet to constraint its stringy corrections at strong coupling in the planar limit. Then we use this four point function to compute corrections to the anomalous dimension of double trace operators of the Lagrangian density and to compute energy-energy correlators at strong coupling.

Paper Structure

This paper contains 14 sections, 89 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Lagrangian four-point function at strong coupling
  3. Extracting CFT data
  4. Anomalous dimension of double trace operators
  5. Unprotected operators
  6. Event shapes in $\mathcal{N}=4$ SYM
  7. Conclusions and discussion
  8. Four point function of $\mathcal{O}(x,y)$
  9. $SU(4)$ channels
  10. Symmetry and analyticity properties of the Mellin amplitude $M_{F}(s,t)$
  11. Dilaton Four point function from $F(u,v)$
  12. Relation between Mellin amplitudes
  13. Rewriting flat space limit in terms of $M_{F}$
  14. Borel Ressumation

Figures (2)

  • Figure 1: Chew-Frautschi plot of the spectrum of exchanged particles in the Virasoro-Shapiro amplitude.
  • Figure 2: The physical picture is the following: excite the vacuum with the state $\mathcal{O}_{\textrm{20}}$ and then measure the flow of energy or $R$ charge with the detector standing in the direction $\vec{n}$ and $\vec{n}'$ at infinity.