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

Abstract

We consider α′ corrections to four-point correlators of half-BPS operators in N\[ \mathcal{N} \] = 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 O2O2OpOp\[ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2{\mathcal{O}}_p{\mathcal{O}}_p\right\rangle \] 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 O2O3Op−1Op\[ \left\langle {\mathcal{O}}_2{\mathcal{O}}_3{\mathcal{O}}_p-1{\mathcal{O}}_p\right\rangle \].