We study monodromy defects in $O(N)$ symmetric scalar field theories $d$ dimensions. After a Weyl transformation, defect may be described by placing the theory on $S^1\times H^{d-1}$, where $H^{d-1}$ is hyperbolic space, and imposing fundamental fields twisted periodicity condition along $S^1$. In this description, codimension two lies at boundary of $H^{d-1}$. first general free theory, then d...

We describe a new method of constructing Kobayashi-hyperbolic surfaces in complex projective 3-space based on deforming surfaces with a " hyperbolic non-percolation " property. We use this method to show that general small deformations of certain singular abelian surfaces of degree 8 are hyperbolic. We also show that a union of 15 planes in general position in projective 3-space admits hyperbol...

We describe a new method of constructing Kobayashi-hyperbolic surfaces in complex projective 3-space based on deforming surfaces with a “hyperbolic non-percolation” property. We use this method to show that general small deformations of certain singular abelian surfaces of degree 8 are hyperbolic. We also show that a union of 15 planes in general position in projective 3-space admits hyperbolic...

A large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. Thes...