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

Abstract

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. The final section focusses on modular graph functions. These are modular functions that are closely associated with coefficients in the low-energy expansion of superstring perturbation theory and have recently received quite a lot of interest in both the physics and mathematics literature.

arXiv comment45 pages, see also the overview article arXiv:2203.13011. v3: journal version

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Cited by in corpus (9)

• The SAGEX Review on Scattering Amplitudes
• Modular-invariant large-$N$ completion of an integrated correlator in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• Higher Derivative Supergravities in Diverse Dimensions
• Generating functions and large-charge expansion of integrated correlators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• Laplace-difference equation for integrated correlators of operators with general charges in $\mathcal{N}=4$ SYM
• Modular graph forms from equivariant iterated Eisenstein integrals
• Visions in Quantum Gravity
• Non-planar integrated correlator in $\mathcal{N}=4$ SYM
• Modular Features of Superstring Scattering Amplitudes: Generalised Eisenstein Series and Theta Lifts