The vacuum moduli spaces of the improved bifundamental SCFTs are claimed to be single-branch irreducible varieties, with Hilbert series extracted from superconformal index limits.
The Hilbert series of 3d N=2 Yang-Mills theories with vectorlike matter
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abstract
This paper presents a formula for the Hilbert series that counts gauge invariant chiral operators in 3d N=2 Yang-Mills theories with vectorlike matter and no Chern-Simons interactions. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background, which is determined by the Higgs mechanism. The sum over magnetic charges is restricted due to instanton effects that partially lift the classical Coulomb branch. The formalism is applied to unitary and symplectic gauge theories with fundamental matter, reproducing old results for the moduli space of vacua and the chiral ring, without resorting to any further effective superpotential on the moduli space.
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Hilbert Series and Superconformal Indices of the Improved Bifundamentals
The vacuum moduli spaces of the improved bifundamental SCFTs are claimed to be single-branch irreducible varieties, with Hilbert series extracted from superconformal index limits.