Abstract
We compute the planar limit of both the free energy and the expectation value of the 1/2 BPS wilson loop for four dimensional \( \mathcal{N} \) = 2 superconformal quiver theories, with a product of SU(N)s as gauge group and hi-fundamental matter. Supersymmetric localization reduces the problem to a multi-matrix model, that we rewrite in the zero instanton sector as an effective action involving an infinite number of double-trace terms, determined by the relevant extended Cartan matrix. We find that the results, as in the case of \( \mathcal{N} \) = 2 SCFTs with a simple gauge group, can be written as sums over tree graphs. For the \( \hat{A_1} \) case, we find that the contribution of each tree can be interpreted as the partition function of a generalized Ising model defined on the tree; we conjecture that the partition functions of these models defined on trees satisfy the Lee-Yang property, i.e. all their zeros lie on the unit circle.
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Fiol, B., Martfnez-Montoya, J. & Fukelman, A.R. The planar limit of \( \mathcal{N} \) = 2 superconformal quiver theories. J. High Energ. Phys. 2020, 161 (2020). https://doi.org/10.1007/JHEP08(2020)161
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DOI: https://doi.org/10.1007/JHEP08(2020)161