From 3d dualities to 2d free field correlators and back

Understand

We investigate the relation between 3d N=2 theories and 2d free field correlators or Dotsenko-Fateev (DF) integrals for Liouville CFT.

• We show that the S^2xS^1 partition functions of some known 3d Seiberg-like dualities reduce, in a suitable 2d limit, to known basic duality identities for DF correlators.
• These identities are applied in a variety of contexts in CFT, as for example in the derivation of the DOZZ 3-point function.
• Reversing the logic, we can try to guess new 3d IR dualities which reduce to more intricate duality relations for the DF correlators.