BCFT One-point Functions of Coulomb Branch Operators - Davide Bason; Lorenzo Di Pietro; Roberto Valandro; Jesse van Muiden (Journal of High Energy Physics)
Abstract We show that supersymmetry can be used to compute the BCFT one-point function coefficients for chiral primary operators, in 4d N $$ \mathcal{N} $$ = 2 SCFTs with 1 2 $$ \frac{1}{2} $$ -BPS boundary conditions. The main ingredient is the hemisphere partition function, with the boundary condition on the equatorial S 3. A supersymmetric Ward identity relates derivatives with respect to the chiral coupling constants to the insertion of the primaries at the pole of the hemisphere. Exact results for the one-point functions can be then obtained in terms of the localization matrix model. We discuss in detail the example of the super Maxwell theory in the bulk, interacting with 3d N $$ \mathcal{N} $$ = 2 SCFTs on the boundary. In particular we derive the action of the SL(2,ℤ) duality on the one-point functions.