Surface Operators and Separation of Variables

Understand

Alday, Gaiotto, and Tachikawa conjectured relations between certain 4d N=2 supersymmetric field theories and 2d Liouville conformal field theory.

• We study generalizations of these relations to 4d theories with surface operators.
• For one type of surface operators the corresponding 2d theory is the WZW model, and for another type - the Liouville theory with insertions of extra degenerate fields.
• We show that these two 4d theories with surface operators exhibit an IR duality, which reflects the known relation (the so-called separation of variables) between the conformal blocks of the WZW model and the Liouville theory.