Abstract
We obtain the perturbative expansion of the free energy on S4 for four dimensional Lagrangian \( \mathcal{N} \) = 2 superconformal field theories, to all orders in the ’t Hooft coupling, in the planar limit. We do so by using supersymmetric localization, after rewriting the 1-loop factor as an effective action involving an infinite number of single and double trace terms. The answer we obtain is purely combinatorial, and involves a sum over tree graphs. We also apply these methods to the perturbative expansion of the free energy at finite N , and to the computation of the vacuum expectation value of the 1/2 BPS circular Wilson loop, which in the planar limit involves a sum over rooted tree graphs.
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Fiol, B., Martínez-Montoya, J. & Fukelman, A.R. The planar limit of \( \mathcal{N} \) = 2 superconformal field theories. J. High Energ. Phys. 2020, 136 (2020). https://doi.org/10.1007/JHEP05(2020)136
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DOI: https://doi.org/10.1007/JHEP05(2020)136