Superconformal Two-Point Functions of the Nahm Pole Defect in $\mathcal{N}=4$ Super-Yang-Mills Theory

Abstract

We derive a manifestly superconformal expression for the leading-order two-point functions of all single trace chiral primary operators in 4d $\mathcal{N}=4$ super-Yang-Mills theory with a co-dimension one Nahm pole defect. Notably, our result involves only a finite number of superblocks that correspond to 1/2-BPS representations in the defect channel. The derivation builds on a non-trivial exact result for traces of fuzzy spherical harmonics in combination with powers of $\mathfrak{su}(2)$ generators, which leads to a remarkably compact expression for the bulk-to-defect couplings. Apart from being interesting in its own right as a closed-form expression at finite $N$, the final result is an essential prerequisite for applying the defect superconformal bootstrap programme to this model.