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

Abstract

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

arXiv comment23 pages plus appendix, 7 figures, v4 fixed typos

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• The planar limit of integrated 4-point functions
• Integrated correlators at strong coupling in an orbifold of $\mathcal{N}=4$ SYM
• Integrated correlators with a Wilson line in a $\mathcal{N}=2$ quiver gauge theory at strong coupling
• Integrated correlators of coincident Wilson lines in $SU(N)$ gauge theories at strong coupling
• Superconformal blocks for stress-tensor and chiral operators for 4D $\mathcal{N}=2$ superconformal field theories
• Constraining $A\to ZH$ with $H\to t\bar{t}$ in the Low-Mass Region