Chiral algebras, localization and surface defects

Abstract

Abstract Four-dimensional N $$ \mathcal{N} $$ = 2 superconformal quantum field theories contain a subsector carrying the structure of a chiral algebra. Using localization techniques, we show for the free hypermultiplet that this structure can be accessed directly from the path integral on the four-sphere. We extend the localization computation to include supersymmetric surface defects described by a generic 4d/2d coupled system. The presence of a defect corresponds to considering a module of the chiral algebra: our results provide a calculational window into its structure constants.

Keywords

• Conformal Field Theory
• Supersymmetric Gauge Theory
• Extended Supersymmetry
• Supersymmetry and Duality