Establish the three-dimensional infrared flow and supersymmetry enhancement

Establish that the proposed three-dimensional \(\mathcal N=2\) abelian Chern–Simons matter theories with gauge group \(U(1)^{4n-1}\) and monopole superpotential \(W_n\) flow to the \(R\)-twisted reductions of the \((A_2,D_{3n-2})\) theories, including the claimed infrared \(\mathcal N=4\) supersymmetry enhancement and Coulomb-branch structure.

Background

The Nahm-sum formula leads to a candidate ultraviolet three-dimensional N=2\mathcal N=2 Chern–Simons matter theory with a specifically determined monopole superpotential. The paper computes its Coulomb-branch chiral ring as a candidate C2/Z2\mathbb C^2/\mathbb Z_2 singularity and finds index terms consistent with enhancement to N=4\mathcal N=4 supersymmetry.

These conclusions are supported by protected, finite-order calculations rather than a direct analysis of the renormalization-group flow. The unresolved problem is to prove the infrared identification and determine how the first nn-dependent operators appear beyond the universal low-order index terms.

References

There are three natural directions for further study. First, the proposed SCFT/VOA correspondence should be strengthened by computing the BRST cohomology, including its strong generators and operator products. Second, the 3d flow and the \mathcal N=4 enhancement should be established beyond the finite-order index tests, and it would be useful to determine how the first n-dependent operators arise.

— SCFT/VOA correspondence and R-twisted reductions of $(A_2,D_{3n-2})$ Argyres--Douglas theories  (2609.04099 - Yoshida, 3 Sep 2026) in Section 7, Summary and discussion