Maximal $U(1)_Y$-violating $n$-point correlators in $\mathcal{N}=4$ super-Yang-Mills theory

Understand

This paper concerns a special class of $n$-point correlation functions of operators in the stress tensor supermultiplet of $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory.

• These are "maximal $U(1)_Y$-violating" correlators that violate the bonus $U(1)_Y$ charge by a maximum of $2(n-4)$ units.
• We will demonstrate that such correlators satisfy $SL(2,\mathbb{Z})$-covariant recursion relations that relate $n$-point correlators to $(n-1)$-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory.
• These recursion relations are used to determine terms in the large-$N$ expansion of $n$-point maximal $U(1)_Y$-violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and $(n-4)$ chiral Lagrangian operators, starting from known properties of the $n=4$ case.