Monodromy Defects in Maximally Supersymmetric Yang-Mills Theories from Holography

We study three Type II supergravity solutions holographically dual to codimension-2 supersymmetric defects in $(p+1)$-dimensional SU($N$) maximally supersymmetric Yang-Mills theory ($p=2,3,4$). In all of these cases, the defects have a non-trivial monodromy for the maximal abelian subgroup for the SO($9-p$) R-symmetry. Such solutions are obtained by considering branes wrapping spindle configurations, changing the parameters (which alters the coordinate domain), and imposing suitable boundary conditions. We provide a prescription to compute the entanglement entropy of the effective theory on the defect. We find the resulting quantity to be proportional to the free energy of the ambient theory. A similar analysis is performed for the D5-brane wrapping a spindle, but we find that changing the coordinate domain does not lead to a defect solution, but rather to a circle compactification.