3d Chern--Simons matter theories from generalized Argyres--Douglas theories

We study 3d $\mathcal{N}=2$ Chern--Simons matter theories describing the R-twisted $S^1$-reduction of Argyres--Douglas theories of $(A_{M-1},A_{N-1})$ type with $\text{gcd}(M,N)=1$, via a recently-proposed 4d/3d correspondence. In particular, for the $(A_2,A_{N-1})$ and $(A_3,A_{N-1})$ theories, we identify a series of Chern--Simons matter theories with monopole superpotentials consistent with an $\mathcal{N}=4$ supersymmetry enhancement in the infrared. As a by-product, we also find a novel Nahm sum formula for the vacuum character of $(3,8)$ $W_3$ minimal model, from which we find another Chern--Simons matter theory describing the R-twisted $S^1$-reduction of the $(A_2,A_4)$ theory.