Gluon scattering in AdS at finite string coupling from localization
Connor Behan, Shai M. Chester, Pietro Ferrero
Abstract
A bstract We consider gluons scattering in Type IIB string theory on AdS 5 × S 5 / ℤ 2 in the presence of D7 branes, which is dual to the flavor multiplet correlator in a certain 4d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 USp(2 N ) gauge theory with SO(8) flavor symmetry and complexified coupling τ . We compute this holographic correlator in the large N and finite τ expansion using constraints from derivatives of the mass deformed sphere free energy, which we compute to all orders in 1 /N and finite τ using supersymmetric localization. In particular, we fix the F 4 higher derivative correction to gluon scattering on AdS at finite string coupling τ s = τ in terms of Jacobi theta functions, which feature the expected relations between the SL(2 , 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 τ 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.