$A_n$-Triality

Understand

A_n-type AGT correspondence anticipates that conformal blocks of A_n Toda CFT are related to partition functions of a family of 4d N=2 SCFTs.

• We use gauge/vortex duality to both give a precise form of the correspondence, and to prove it.
• Gauge/vortex duality relates the 4d theories and the 2d theories living on its vortices.
• Partition functions of the 2d theories on vortices provide Coulomb-gas representation of A_n Toda conformal blocks with discrete internal momenta.