We propose a renormalization group flow with emergent supersymmetry in two dimensions from a non-Lagrangian theory. The ultraviolet theory does not have supersymmetry while the infrared theory does. The flow is constrained analytically by topological defect lines including a new spin constraint, and further supported by numerics from the truncated conformal space approach.

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We give sharp estimates for the fractional maximal function in terms of Hausdorff capacity. At the same time we identify the real interpolation spaces between$L$_{1}and the Morrey space $\mathcal{L}^{1,\lambda}$ . The result can be viewed as an analogue of the Hardy–Littlewood maximal theorem for the fractional maximal function.

Let X and Y be two complex manifolds, let$D$⊂$X$and$G$⊂$Y$be two nonempty open sets, let$A$(resp.$B$) be an open subset of ∂$D$(resp. ∂$G$), and let$W$be the 2-fold cross (($D$∪$A$)×$B$)∪($A$×($B$∪$G$)). Under a geometric condition on the boundary sets$A$and$B$, we show that every function locally bounded, separately continuous on$W$, continuous on$A$×$B$, and separately holomorphic on ($A$×$G$)∪($D$×$B$) “extends” to a function continuous on a “domain of holomorphy” $\widehat{W}$ and holomorphic on the interior of $\widehat{W}$ .