The SAGEX Review on Scattering Amplitudes, Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their $\mathcal{N}=4$ supersymmetric Yang-Mills duals

Understand

This article reviews some results of the SAGEX programme that have developed in the understanding of the interplay of supersymmetry and modular covariance of scattering amplitudes in type IIB superstring theory and its holographic image in $\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM).

• The first section includes the determination of exact expressions for BPS interactions in the low-energy expansion of type IIB superstring amplitudes.
• The second section concerns properties of a certain class of integrated correlators in $\mathcal{N}=4$ SYM with arbitrary classical gauge group that are exactly determined by supersymmetric localisation.
• Not only do these reproduce known features of perturbative and non-perturbative $\mathcal{N}=4$ SYM for any classical gauge group, but they have large-$N$ expansions that are in accord with expectations based on the holographic correspondence with superstring theory.