String corrections to AdS amplitudes and the double-trace spectrum of N=4 SYM

Abstract

We consider ${\alpha }^{\prime }$ corrections to four-point correlators of half-BPS operators in $\mathcal{N}=4$ super Yang-Mills theory in the supergravity limit. By demanding the correct behaviour in the flat space limit, we find that the leading $({\alpha }^{\prime }{)}^3$ correction to the Mellin amplitude is fixed for arbitrary charges of the external operators. By considering the mixing of double-trace operators we can find the $({\alpha }^{\prime }{)}^3$ corrections to the double-trace spectrum which we give explicitly for $su(4)$-singlet operators. We observe striking patterns in the corrections to the spectra which hint at their common ten-dimensional origin. By extending the observed patterns and imposing them at order $({\alpha }^{\prime }{)}^5$ we are able to reproduce the recently found result for the correction to the Mellin amplitude for $⟨{\mathcal{O}}_2{\mathcal{O}}_2{\mathcal{O}}_p{\mathcal{O}}_p⟩$ correlators. By applying a similar logic to the $[0,1,0]$ channel of $su(4)$ we are able to deduce new results for the correlators of the form $⟨{\mathcal{O}}_2{\mathcal{O}}_3{\mathcal{O}}_{p-1}{\mathcal{O}}_p⟩$.

arXiv comment28 pages; v2: minor changes and improved discussion, journal version

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