Weak Coupling Limits and Colliding Punctures in Class-S Theories

Understand

Class-S theories are four-dimensional N=2 supersymmetric field theories constructed by the reduction of a (2,0) six-dimensional theory on a punctured Riemann surface C (called the UV curve).

• A basic degeneration limit of the surface C is when several punctures are brought close to each other.
• As this happens, a long tube appears in C and a weakly coupled gauge group emerges.
• When the corresponding gauge coupling is turned off, we are left with two surfaces.