Abstract
We discuss aspects of theories with superpotentials given by Arnold’s A, D, E singularities, particularly the novelties that arise when the fields are matrices. We focus on 4d \( \mathcal{N}=1 \) variants of susy QCD, with U(N c ) or SU(N c ) gauge group, N f fundamental flavors, and adjoint matter fields X and Y appearing in W A,D,E (X, Y) superpotentials. Many of our considerations also apply in other possible contexts for matrix-variable W A,D,E . The 4d W A,D,E SQCD-type theories RG flow to superconformal field theories, and there are proposed duals in the literature for the \( {W}_{A_k} \), \( {W}_{D_k} \), and \( {W}_{E_7} \) cases. As we review, the \( {W}_{D_{\mathrm{even}}} \) and \( {W}_{E_7} \) duals rely on a conjectural, quantum truncation of the chiral ring. We explore these issues by considering various deformations of the W A,D,E superpotentials, and the resulting RG flows and IR theories. Rather than finding supporting evidence for the quantum truncation and \( {W}_{D_{\mathrm{even}}} \) and \( {W}_{E_7} \) duals, we note some challenging evidence to the contrary.
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Intriligator, K., Nardoni, E. Deformations of W A,D,E SCFTs. J. High Energ. Phys. 2016, 43 (2016). https://doi.org/10.1007/JHEP09(2016)043
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DOI: https://doi.org/10.1007/JHEP09(2016)043