# Wilson Loops and Wormholes

**Authors:** Panos Betzios, Olga Papadoulaki  
**arXiv:** [2311.09289](https://arxiv.org/abs/2311.09289)  
**Date:** 2023-11-15  
**Summary page:** https://www.summarizepaper.com/en/paper/2311.09289v1/

## Key points

- Authors investigate properties of Wilson loop observables in holographic gauge theories
- Focus on cases with single and/or multiple boundaries (Euclidean wormholes)
- Generalize and refine previous characterizations based on compressibility of cycles and pinching limit of higher genus Riemann surfaces
- Analysis provides insights into dynamics and phase structure of dual gauge theory
- Wilson loop observables carry important information about system behavior
- Backreacting correlated observables (e.g., Wilson loops) can lead to Euclidean wormhole saddles in dual gravitational path integral
- Leveraging representation theoretic entanglement structure proposed in previous works
- Contributes to understanding of Wilson loop observables with Euclidean wormhole geometries
- Expands upon previous characterizations by considering compressibility of cycles and pinching limits on higher genus Riemann surfaces
- Highlights influence of these observables on dual gravitational path integral, providing new insights into their behavior

## Summary

In the paper "Wilson Loops and Wormholes," authors Panos Betzios and Olga Papadoulaki investigate the properties of Wilson loop observables in holographic gauge theories. Specifically, they focus on cases where the dual bulk geometries have single and/or multiple boundaries, known as Euclidean wormholes. By studying these observables, the authors aim to generalize and refine previous characterizations based on the compressibility of cycles and the pinching limit of higher genus Riemann surfaces. The analysis of Wilson loop observables in holographic gauge theories provides valuable insights into the dynamics and phase structure of the corresponding dual gauge theory, regardless of its dimensionality. These observables carry important information about the behavior of the system under study. Furthermore, Betzios and Papadoulaki explore how backreacting correlated observables, such as Wilson loops, can lead to Euclidean wormhole saddles in the dual gravitational path integral. This phenomenon is achieved by leveraging a representation theoretic entanglement structure proposed in previous works (arXiv:2110.14655 and arXiv:2204.01764). Overall, this paper contributes to our understanding of Wilson loop observables in holographic gauge theories with Euclidean wormhole geometries. The findings expand upon previous characterizations by considering compressibility of cycles and pinching limits on higher genus Riemann surfaces. The authors also highlight how these observables can influence the dual gravitational path integral through backreacting correlations, leading to Euclidean wormhole saddles that provide new insights into their behavior under study.