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We present numerical experiments that test the predictions of a conjecture of Gaiotto–Moore–Neitzke and Gaiotto concerning the monodromy map for opers, the non-Abelian Hodge correspondence, and the restriction of the hyperkähler L2 metric to the Hitchin section. These experiments are conducted in the setting of polynomial holomorphic differentials on the complex plane, where the predictions take the form of conjectural formulas for the Stokes data and the metric tensor. Overall, the results of our experiments support the conjecture. 

A bstract Given a 4d $$ \mathcal{N} $$ N = 2 superconformal theory with an $$ \mathcal{N} $$ N = (2 , 2) superconformal surface defect, a marginal perturbation of the bulk theory induces a complex structure deformation of the defect moduli space. We describe a concrete way of computing this deformation using the bulk-defect OPE. 

A bstract It is known that some theories of class S are actually factorized into multiple decoupled nontrivial four-dimensional $$ \mathcal{N} $$ N = 2 theories. We propose a way of constructing examples of this phenomenon using the physics of half-BPS surface defects, and check that it works in one simple example: it correctly reproduces a known realization of two copies of $$ \mathcal{N} $$ N = 2 superconformal SU(2) QCD, describing this factorized theory as a class S theory of type A 3 on a five-punctured sphere with a twist line. Separately, we also present explicit checks that the Coulomb branch of a putative factorized class S theory has the expected product structure, in two examples.