Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills

Understand

The four dimensional $\mathcal{N}=4$ super-Yang-Mills (SYM) theory exhibits rich dynamics in the presence of codimension-one conformal defects.

• The new structure constants of the extended operator algebra consist of one-point functions of local operators which are nonvanishing due to the defect insertion and carry nontrivial coupling dependence.
• We study an important class of half-BPS superconformal defects engineered by D5 branes that share three common directions with the D3 branes and involve Nahm pole configurations for the SYM fields on the D3 brane worldvolume.
• In the planar large $N$ limit, we obtain non-perturbative results in the 't Hooft coupling $\lambda$ for the defect one-point functions of both BPS and non-BPS operators, building upon recent progress in localization and integrability methods.