5D SYM and 2D q-deformed YM

We study the AGT-like conjectured relation of a four-dimensional gauge theory on S3×S1S3×S1 to two-dimensional q-deformed Yang–Mills theory on a Riemann surface Σ   by using a five-dimensional N=2N=2 supersymmetric Yang–Mills theory on S3×ΣS3×Σ, following the conjectured relation of the six-dimensional N=(2,0)N=(2,0) theory on S1S1 to the five-dimensional Yang–Mills theory. Our results are in perfect agreement with both of the conjectures.