AdS Virasoro-Shapiro from single-valued periods
Luis F. Alday, Tobias Hansen, Joao A. Silva
Abstract
A bstract We determine the full 1 / $$ \sqrt{\uplambda} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>λ</mml:mi> </mml:msqrt> </mml:math> correction to the flat-space Wilson coefficients which enter the AdS Virasoro-Shapiro amplitude in $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM theory at strong coupling. The assumption that the Wilson coefficients are in the ring of single-valued multiple zeta values, as expected for closed string amplitudes, is surprisingly powerful and leads to a unique solution to the dispersive sum rules relating Wilson coefficients and OPE data obtained in [1]. The corresponding OPE data fully agrees with and extends the results from integrability. The Wilson coefficients to order 1 / $$ \sqrt{\uplambda} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>λ</mml:mi> </mml:msqrt> </mml:math> can be summed into an expression whose structure of poles and residues generalises that of the Virasoro-Shapiro amplitude in flat space.