AdS Virasoro-Shapiro amplitude with KK modes
Giulia Fardelli, Tobias Hansen, Joao A. Silva
Abstract
A bstract We determine the first curvature correction for the string amplitude of two supergravity states and two Kaluza-Klein modes on AdS 5 ×S 5 , which is dual to the correlator $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2{\mathcal{O}}_p{\mathcal{O}}_p\right\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> of half-BPS operators in $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM theory. The result has the form of an integral over the Riemann sphere as for the usual Virasoro-Shapiro amplitude, with the insertion of single-valued multiple polylogarithms of weight three. The result fixes OPE data of single-trace operators 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, including operators with non-zero R -charge and odd spin. We successfully check our results by comparing to data available from integrability, localisation and consistency with a 10 d effective action.