# Universal Entanglement and Boundary Geometry in Conformal Field Theory

**Authors:** Christopher P. Herzog, Kuo-Wei Huang, Kristan Jensen  
**arXiv:** [1510.00021](https://arxiv.org/abs/1510.00021)  
**Date:** 2015-09-30  
**Summary page:** https://www.summarizepaper.com/en/paper/1510.00021v3/

## Key points

- Authors Herzog, Huang, and Jensen study universal contribution to vacuum entanglement entropy in even-dimensional conformal field theory
- Use conformal map to hyperbolic space crossing a circle to address challenges in deriving entanglement entropy
- Universal part of entanglement entropy seen as purely boundary effect
- Calculate universal contribution and derive explicit form for A-type anomaly contribution to Wess-Zumino term for trace anomaly
- Boundary terms generalize earlier bulk actions in dimensions d=4 and 6, emphasizing role of boundary geometry
- Insights into relationship between boundary effects and universal contributions offer new perspectives on theoretical physics research

## Summary

In their paper titled "Universal Entanglement and Boundary Geometry in Conformal Field Theory," authors Christopher P. Herzog, Kuo-Wei Huang, and Kristan Jensen explore the universal contribution to the vacuum entanglement entropy (EE) across a sphere in even-dimensional conformal field theory. They employ a conformal map to hyperbolic space crossing a circle to address previous challenges related to deriving the EE. This is due to a lack of understanding of the appropriate boundary terms in the trace anomaly. The key insight presented in this work is that the universal part of the entanglement entropy can be viewed as a purely boundary effect. Through their computations, the authors not only calculate this universal contribution but also derive an explicit form for the A-type anomaly contribution to the Wess-Zumino term for the trace anomaly, now incorporating boundary terms into the analysis. In dimensions d=4 and 6, Herzog et al. demonstrate that these boundary terms generalize earlier bulk actions found in existing literature, shedding light on how boundary geometry plays a crucial role in understanding entanglement entropy within conformal field theory. This expansion on previous findings provides valuable insights into the intricate relationship between boundary effects and universal contributions to entanglement entropy in conformal field theory, offering new perspectives on how these concepts intertwine within theoretical physics research.