(De)constructing Intersecting M5-branes

We describe intersecting M5-branes, as well as M5-branes wrapping the holomorphic curve $xy=c,$ in terms of a limit of a defect conformal field theory (dCFT) with two-dimensional (4,0) supersymmetry. This defect CFT describes the low-energy theory of intersecting D3-branes at a ${C}^{2}/{Z}_{k}$ orbifold. In an appropriate $\stackrel{\ensuremath{\rightarrow}}{k}\ensuremath{\infty}$ limit, two compact spatial directions are generated. By identifying moduli of the M5-M5 intersection in terms of those of the defect CFT, we argue that the ${\mathrm{SU}(2)}_{L}R$ symmetry of the (4,0) defect CFT matches the $\mathrm{SU}(2)R$ symmetry of the $\mathcal{N}=2,d=4$ theory of the M5-M5 intersection. We find a 't Hooft anomaly in the ${\mathrm{SU}(2)}_{L}R$ symmetry, suggesting that tensionless strings give rise to an anomaly in the $\mathrm{SU}(2)R$ symmetry of intersecting M5-branes.