Boundary layers and one-point functions in the presence of monodromy defects

A bstract We study one-point functions of composites of charge e operators in the presence of a monodromy defect for a U (1) global symmetry with monodromy β . We first compute these in free massless and massive theories, recovering in the former case the known sin( eπβ ) dependence and obtaining in the latter a sin 2 ( eπβ ) dependence. We then turn to holography and compute 1-point functions for operators O of charge J = ∆ in su(N) su N N N = 4 SYM in the presence of a monodromy defect for a U (1) ∈ SO (6) R . From a WKB analysis in large ∆ we recover the structure of standard and anchored saddles previously found in the literature, finding that, to subleading order in 1/∆, the anchored regime is resolved by a boundary layer effect. Finally, using heat kernel methods, we determine the monodromy dependence of the induced 1-point function for the composite O † O , finding a smooth sin 2 ( Jπβ ) behavior.