# Covert Symmetry Breaking

**Authors:** C. W. Erickson, A. D. Harrold, Rahim Leung, K. S. Stelle  
**arXiv:** [2007.12192](https://arxiv.org/abs/2007.12192)  
**Date:** 2020-07-23  
**Summary page:** https://www.summarizepaper.com/en/paper/2007.12192v1/

## Key points

- Investigate covert symmetry breaking in the context of reduction from higher-dimensional to lower-dimensional field theory
- Ground state of the system has nontrivial dependence on reduction coordinates
- Focus on a simple model of $(d+1)$-dimensional scalar QED with restricted dimension and boundary conditions
- Effective $d$-dimensional theory with Maxwellian dynamics at free theory level
- Unusual symmetry breaking occurs in quartic vector-scalar interaction terms of reduced theory
- Symmetry breaking only apparent at fourth order in lower-dimensional effective field theory action
- Similar effects observed in gravitational braneworld scenarios, making model relevant for understanding complex scenarios
- Study sheds light on mechanism behind covert symmetry breaking and its occurrence in reduced field theories with nontrivial ground state dependence on reduction coordinates
- Findings contribute to understanding how symmetries manifest differently in different dimensions and provide insights into gravitational braneworld scenarios.

## Summary

In this study, the authors investigate the phenomenon of covert symmetry breaking in the context of reduction from a higher-dimensional to a lower-dimensional field theory. They explore how special features can arise when the ground state of the system has nontrivial dependence on the reduction coordinates. The authors focus on a simple model of $(d+1)$-dimensional scalar QED (quantum electrodynamics) with one dimension restricted to an interval with Dirichlet/Robin boundary conditions on opposing ends. This setup leads to an effective $d$-dimensional theory with Maxwellian dynamics at the free theory level. However, they find that unusual symmetry breaking occurs in the quartic vector-scalar interaction terms of this reduced theory. What makes this phenomenon interesting is that the symmetry breaking only becomes apparent at fourth order in the lower-dimensional effective field theory action. This delayed "covert" form of spontaneous symmetry breaking reveals itself only after reducing from higher dimensions and analyzing interactions at higher orders. The authors note that similar effects have been observed in gravitational braneworld scenarios, making their simple model relevant for understanding these more complex scenarios as well. Overall, this study sheds light on the mechanism behind covert symmetry breaking and highlights its occurrence in reduced field theories with nontrivial ground state dependence on reduction coordinates. The findings contribute to our understanding of how symmetries can manifest differently in different dimensions and provide insights into gravitational braneworld scenarios.