# Holographic Subregion Complexity for Singular Surfaces

## TL;DR

This paper investigates the divergence structure and universal terms of holographic subregion complexity for singular surfaces, revealing new universal logarithmic terms and divergent behaviors due to surface singularities.

## Contribution

It analyzes the divergence structure of holographic subregion complexity for various singular surfaces, identifying new universal and divergent terms caused by singularities.

## Key findings

- Discovery of new universal logarithmic terms due to surface singularities
- Identification of novel divergent terms like square logarithm and negative powers with logs
- Analysis of complexity for kink and cone-shaped subregions in different dimensions

## Abstract

Recently holographic prescriptions are proposed to compute quantum complexity of a given state in the boundary theory. A specific proposal known as `holographic subregion complexity' is supposed to calculate the the complexity of a reduced density matrix corresponding to a static subregion. We study different families of singular subregions in the dual field theory and find the divergence structure and universal terms of holographic subregion complexity for these singular surfaces. We find that there are new universal terms, logarithmic in the UV cutoff, due to the singularities of a family of surfaces including a kink in (2+1)-dimension and cones in even dimensional field theories. We find examples of new divergent terms such as square logarithm and negative powers times the logarithm of the UV cut-off parameter.