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From Weyl Anomaly to Universal Defect Casimir Energy and Rényi Entropy
Zi-Xiao Huang1, Ma-Ke Yuan1, Yang Zhou1,2,3
1Fudan University, Department of Physics and Center for Field Theory and Particle Physics, Shanghai 200433, China.
Physical Review Letters
|June 7, 2026
Summary
We found universal relationships between surface defect anomalies and quantum field theory properties. These findings link defect anomalies to Casimir energy and entanglement structure in higher dimensions.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- String Theory
Background:
- Surface defects in quantum field theories exhibit unique properties.
- Understanding anomalies is crucial for characterizing field theories.
- Supersymmetric quantum field theories (SQFTs) offer a framework for studying these phenomena.
Purpose of the Study:
- To establish universal relations between surface defect Weyl anomalies and fundamental properties like ground state energy and entanglement.
- To provide concrete examples in higher-dimensional SQFTs, specifically 6d superconformal field theories (SCFTs).
- To develop a comprehensive method applicable to broader SCFTs with defects.
Main Methods:
- Utilizing supersymmetric localization techniques.
- Analyzing anomaly polynomials.
- Employing holographic duality (AdS/CFT correspondence).
Main Results:
- Derived universal relations connecting surface defect Weyl anomalies (b and d_{2}) to the defect contribution to supersymmetric Casimir energy in 6d SCFTs.
- Obtained a closed-form expression for the defect contribution to supersymmetric Rényi entropy.
- Demonstrated the applicability of the developed method to various SCFTs with defects.
Conclusions:
- The study establishes a powerful framework for understanding the interplay between anomalies and physical observables in SQFTs with defects.
- The derived relations offer new insights into the structure of entanglement and energy in these complex systems.
- The methodology provides a versatile tool for future investigations of quantum field theories with defects.
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