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Displacement Operators and Constraints on Boundary Central Charges
Christopher Herzog1, Kuo-Wei Huang1,2, Kristan Jensen3
1C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794, USA.
Physical Review Letters
|January 30, 2018
Summary
Boundary conformal field theories reveal new boundary central charges. These charges are constrained using correlation functions of the displacement operator in 3- and 4-dimensional theories.
Area of Science:
- Theoretical physics
- Quantum field theory
- Conformal field theory
Background:
- Boundary conformal field theories (BCFTs) exhibit unique properties not found in their bulk counterparts.
- The trace anomaly of the stress tensor in BCFTs contains additional boundary-specific terms.
- Understanding these boundary terms is crucial for characterizing the theory's behavior near boundaries.
Purpose of the Study:
- To constrain boundary central charges in 3- and 4-dimensional BCFTs.
- To establish a general method for deriving these constraints.
- To explore potential relations between boundary charges and correlation functions.
Main Methods:
- Analyzing the trace anomaly of the stress tensor in BCFTs.
- Calculating two- and three-point correlation functions of the displacement operator.
- Comparing scale-dependent contact terms in correlation functions with the trace anomaly.
Main Results:
- Derived constraints on boundary central charges in terms of correlation functions.
- Provided a general derivation applicable to various BCFTs.
- Conjectured a specific relation between the a-type boundary charge and the stress tensor two-point function in 3D.
Conclusions:
- The study successfully constrained boundary central charges using correlation functions.
- The findings offer a new perspective on the structure of anomalies in BCFTs.
- Verification in free theories supports the generality of the results.
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