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arXiv · 1810.00840

Universality of Toda equation in ${\cal N}=2$ superconformal field theories

Antoine Bourget·Diego Rodriguez-Gomez·Jorge G. Russo
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Abstract

We show that extremal correlators in all Lagrangian ${\cal N}=2$ superconformal field theories with a simple gauge group are governed by the same universal Toda system of equations, which dictates the structure of extremal correlators to all orders in the perturbation series. A key point is the construction of a convenient orthogonal basis for the chiral ring, by arranging towers of operators in order of increasing dimension, which has the property that the associated two-point functions satisfy decoupled Toda chain equations. We explicitly verify this in all known SCFTs based on $\mathrm{SU}(N)$ gauge groups as well as in superconformal QCD based on orthogonal and symplectic groups. As a by-product, we find a surprising non-renormalization property for the ${\cal N}=2$ $\mathrm{SU}(N)$ SCFT with one hypermultiplet in the rank-2 symmetric representation and one hypermultiplet in the rank-2 antisymmetric representation, where the two-loop terms of a large class of supersymmetric observables identically vanish.

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Antoine Bourget, Diego Rodriguez-Gomez, Jorge G. Russo. 2018-10-25. Universality of Toda equation in ${\cal N}=2$ superconformal field theories. https://doi.org/10.1007/jhep02(2019)011

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