Gluon scattering in AdS at finite string coupling from localization

Abstract

We consider gluons scattering in Type IIB string theory on AdS${}_5\times S^5/{\mathbb{Z}}_2$ in the presence of D7 branes, which is dual to the flavor multiplet correlator in a certain 4d $\mathcal{N}=2$ $USp(2N)$ gauge theory with $SO(8)$ flavor symmetry and complexified coupling $\ddot{I}„$. We compute this holographic correlator in the large $N$ and finite $\ddot{I}„$ expansion using constraints from derivatives of the mass deformed sphere free energy, which we compute to all orders in $1/N$ and finite $\ddot{I}„$ using supersymmetric localization. In particular, we fix the $F^4$ higher derivative correction to gluon scattering on AdS at finite string coupling $\ddot{I}{„}_s=\ddot{I}„$ in terms of Jacobi theta functions, which feature the expected relations between the $SL(2,\mathbb{Z})$ duality and the $SO(8)$ triality of the CFT, and match it to the known flat space term. We also use the flat space limit to compute $D^2{F}^4$ corrections of the correlator at finite $\ddot{I}„$ in terms of a non-holomorphic Eisenstein series. At weak string coupling, we find that the AdS correlator takes a form which is remarkably similar to that of the flat space Veneziano amplitude.

26 pages plus appendices, v7 typo fixed