Monodromy Defects from Hyperbolic Space

Understand

We study monodromy defects in $O(N)$ symmetric scalar field theories in $d$ dimensions.

• After a Weyl transformation, a monodromy defect may be described by placing the theory on $S^1\times H^{d-1}$, where $H^{d-1}$ is the hyperbolic space, and imposing on the fundamental fields a twisted periodicity condition along $S^1$.
• In this description, the codimension two defect lies at the boundary of $H^{d-1}$.
• We first study the general monodromy defect in the free field theory, and then develop the large $N$ expansion of the defect in the interacting theory, focusing for simplicity on the case of $N$ complex fields with a one-parameter monodromy condition.