String corrections to AdS amplitudes and the double-trace spectrum of N$$ \mathcal{N} $$ = 4 SYM

We consider α′ 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 (α′)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 (α′)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 (α′)5 we are able to reproduce the recently found result for the correction to the Mellin amplitude for $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2{\mathcal{O}}_p{\mathcal{O}}_p\right\rangle $$ 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 $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_3{\mathcal{O}}_p-1{\mathcal{O}}_p\right\rangle $$.