# On 4d rank-one $$\mathcal{N}=3$$ superconformal field theories

Journal of High Energy Physics, Sep 2016

We study the properties of 4d $$\mathcal{N}=3$$ superconformal field theories whose rank is one, i.e. those that reduce to a single vector multiplet on their moduli space of vacua. We find that the moduli space can only be of the form ℂ3/ℤ ℓ for ℓ=1, 2, 3, 4, 6, and that the supersymmetry automatically enhances to $$\mathcal{N}=4$$ for ℓ=1, 2. In addition, we determine the central charges a and c in terms of ℓ, and construct the associated 2d chiral algebras, which turn out to be exotic $$\mathcal{N}=2$$ supersymmetric W-algebras.

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Takahiro Nishinaka, Yuji Tachikawa. On 4d rank-one $$\mathcal{N}=3$$ superconformal field theories, Journal of High Energy Physics, 2016, 116, DOI: 10.1007/JHEP09(2016)116