Abstract
We continue to investigate the $\mathcal{N}=1$ deformations of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) labeled by a nilpotent element of the flavor symmetry. This triggers a renormalization group (RG) flow to an $\mathcal{N}=1$ SCFT. We systematically analyze all possible deformations of this type for certain classes of $\mathcal{N}=2$ SCFTs: conformal SQCDs, generalized Argyres-Douglas theories and the $E_6$ SCFT. We find a number of examples where the amount of supersymmetry gets enhanced to $\mathcal{N}=2$ at the end point of the RG flow. Most notably, we find that the $SU(N)$ and $Sp(N)$ conformal SQCDs can be deformed to flow to the Argyres-Douglas (AD) theories of type $(A_1, D_{2N-1})$ and $(A_1, D_{2N})$ respectively. This RG flow therefore allows us to compute the full superconformal index of the $(A_1,D_N)$ class of AD theories. Moreover, we find an infrared duality between $\mathcal{N}=1$ theories where the fixed point is described by an $\mathcal{N}=2$ AD theory. We observe that the classes of examples that exhibit supersymmetry enhancement saturate certain bounds for the central charges implied by the associated two-dimensional chiral algebra.
Highlights
We find a number of examples where the amount of supersymmetry gets enhanced to N = 2 at the end point of the renormalization group (RG) flow
We observe that the classes of examples that exhibit supersymmetry enhancement saturate certain bounds for the central charges implied by the associated two-dimensional chiral algebra
We find that when the undeformed N = 2 SCFT is given by an SU(N ) gauge theory with Nf = 2N fundamental hypermultiplets and M is given a vev corresponding to the next-to-principal nilpotent orbit labeled by the partition [N −1, 1] of the SU(2N ) flavor symmetry, the IR fixed point is characterized by the (A1, D2N ) theory
Summary
Recall that in the set-ups considered in [1, 8], the Coulomb branch operators at the IR fixed point arose from the gauge singlet fields that remained coupled to the interacting theory We find that this is the case for the present theories . Set of nilpotent embedding of SU(2N ) for explicit values of N , 2 ≤ N ≤ 10, and found that in most of the cases the central charges of the IR theory are irrational numbers. The flavor symmetry in this case is given by Sp(N − 2) and the deformation is given by coupling a gauge singlet field M in the adjoint representation of Sp(N − 2), to the moment map operator of Sp(N − 2), and giving M a nilpotent vev.
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