  We initiate the study of intersecting surface operators/defects in
four-dimensional quantum field theories (QFTs). We characterize these defects
by coupled 4d/2d/0d theories constructed by coupling the degrees of freedom
localized at a point and on intersecting surfaces in spacetime to each other
and to the four-dimensional QFT. We construct supersymmetric intersecting
surface defects preserving just two supercharges in N = 2 gauge theories. These
defects are amenable to exact analysis by localization of the partition
function of the underlying 4d/2d/0d QFT. We identify the 4d/2d/0d QFTs that
describe intersecting surface operators in N = 2 gauge theories realized by
intersecting M2-branes ending on N M5-branes wrapping a Riemann surface. We
conjecture and provide evidence for an explicit equivalence between the
squashed four-sphere partition function of these intersecting defects and
correlation functions in Liouville/Toda CFT with the insertion of arbitrary
degenerate vertex operators, which are labeled by representations of SU(N).

High Energy Physics - Theory