In this talk, I will discuss correlation functions in 6d (2, 0) theories of two 1/2-BPS operators inserted away from a 1/2-BPS surface defect. In the large central charge limit the leading connected contribution corresponds to sums of tree-level Witten diagram in AdS7×S4 in the presence of an AdS3 defect. I will show that these correlators can be uniquely determined by imposing only superconformal symmetry and consistency conditions, eschewing the details of the complicated effective Lagrangian. I will present the explicit result of all such two-point functions, which exhibits remarkable hidden simplicity.

In this talk, I will discuss AdS super gluon scattering amplitudes in various spacetime dimensions. These amplitudes are dual to correlation functions in a variety of non-maximally supersymmetric CFTs, such as the 6d E-string theory, 5d Seiberg exceptional theories, etc. I will introduce a powerful method based on symmetries and consistency conditions, and show that it fixes all the infinitely many four-point amplitudes at tree level. I will also point out many interesting properties and structures of these amplitudes, which include the flat space limit, Parisi-Sourlas-like dimensional reduction, hidden conformal symmetry, and a color-kinematic duality in AdS. Along the way, I will also review some earlier progress and the relation with this work. I will conclude with a brief discussion of various open problems. [please email alejandro.cabo_bizet@kcl.ac.uk for the zoom link]