# Higher codimension defects A conical defect has codimension 2. It is interesting to consider defects with higher codimensions, which can appear in the context of e.g. string theory conifolds. However, there is a qualitative difference between the codimension-2 case and higher codimensional cases: taking a quotient does not affect the curvature of the cone. ## Refs - for ordinary conical defects - Lovelock (including Einstein) with $U(1)$ symmetry: [[1995#Fursaev, Solodukhin]] - squared cone [[2013#Fursaev, Patrushev, Solodhukin]] - with quadratic gravity as examples - related to - [[0362 Entanglement surface with cusps]] - see also - [[2012#Myers, Singh]] - [[2020#Kastikainen]]: codimension-2$p$ defects in Lovelock