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# Bootstrapping 4d $\mathcal{N}=2$ gauge theories: the case of SQCD

May 2022

We derive exact relations between certain integrals of the conserved flavorcurrent four point function in 4d $\mathcal{N}=2$ conformal field theories(CFTs) and derivatives of the mass deformed sphere free energy, which can becomputed exactly for gauge theories using supersymmetric localization. Forconformal gauge theories with flavor groups of rank greater than one, there areat least two such integrated constraints, which can then be combined with thenumerical conformal bootstrap to bound CFT data as a function of thecomplexified gauge coupling $\tau$. We apply this strategy to the case of$SU(2)$ conformal SQCD with flavor group $SO(8)$, where we compute bounds onunprotected scaling dimensions as a function of $\tau$ that match the freetheory limit, and exhibit the expected mixing between the action of the$SL(2,\mathbb{Z})$ duality group and $SO(8)$ triality.

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