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Recently, it was found that certain 4d $\mathcal{N}=1$ Lagrangians experiencesupersymmetry enhancement at their IR fixed point, thereby giving a Lagrangiandescription for a plethora of Argyres-Douglas theories. A generic feature ofthese Lagrangians is that a number of gauge invariant operators decouple (asfree fields) along the RG-flow. These decoupled operators can be naturallytaken into account from the beginning itself by introducing additional gaugesinglets (sometimes called `flipping fields') that couple to the decoupledoperators via appropriate superpotential terms. It has also been checked thatupon dimensionally reducing to 3d, the $(A_1,A_{2n-1})$ type Lagrangians onlyproduce the expected behavior when flipping fields are included in theLagrangian. In this paper we further investigate the role of flipping fieldsand find an example where the expected necessity of including the flippingfields in the dimensionally reduced Lagrangians seems to get violated. In theprocess we find two new dual Lagrangians for the so called 3d $T[SU(2)]$theory.

On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories