Beem–Rastelli Higgs branch conjecture for four-dimensional N=2 SCFTs

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Let T\mathcal{T} be a four-dimensional N=2N=2 superconformal field theory, let Φ(T)\Phi(\mathcal{T}) be its associated vertex algebra, and let HiggsTHiggs_{\mathcal{T}} denote its Higgs branch. Write XΦ(T)X_{\Phi(\mathcal{T})} for the associated variety of the vertex algebra. Beem–Rastelli conjecture. One has

HiggsT=XΦ(T).Higgs_{\mathcal{T}}=X_{\Phi(\mathcal{T})}.

The conjecture proposes that the Higgs-branch geometry of a four-dimensional N=2N=2 SCFT is exactly captured by the associated variety of its two-dimensional vertex algebra. The supplied text gives examples where the equality is known and says that the general statement is expected, but provides no resolution.

References

Primary source

Tomoyuki Arakawa, “Representation theory of W-algebras and Higgs branch conjecture”, arXiv:1712.07331 (2017).

Additional references

2 papers in this index state this conjecture (2017). The statement above is taken from the most recent of them; the others are arXiv:1712.01945.

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