Conformal field theories in fractional dimensions
Sheer El-Showk1, Miguel Paulos2, David Poland3
1Institut de Physique Théorique CEA Saclay, CNRS-URA 2306, 91191 Gif sur Yvette, France and CERN, Theory Division, CH-1211 Geneva 23, Switzerland.
Physical Review Letters
|April 29, 2014
Summary
We explored conformal field theories in fractional dimensions, finding evidence for a connecting family of models. This research provides predictions for key properties like operator dimensions and central charge.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- Conformal Field Theory
Background:
- Conformal field theories (CFTs) are crucial in understanding critical phenomena and quantum systems.
- Investigating CFTs in fractional dimensions presents unique theoretical challenges and opportunities.
Purpose of the Study:
- To rigorously bound operator dimensions in fractional space-time dimensions using the conformal bootstrap.
- To identify and characterize a potential family of unitary CFTs bridging known models across different dimensions.
Main Methods:
- Application of the conformal bootstrap technique.
- Analysis in fractional space-time dimensions (D).
- Numerical predictions and comparison with established theories.
Main Results:
- Rigorous bounds on operator dimensions were obtained.
- Strong evidence for a family of unitary CFTs connecting the 2D Ising model, 3D Ising model, and 4D free scalar theory was found.
- Numerical predictions for leading operator dimensions and central charge at various D were generated.
Conclusions:
- The study provides a unified framework for understanding related CFTs across dimensions.
- The findings offer testable predictions for operator dimensions and central charge.
- This work advances the application of the conformal bootstrap in exploring complex quantum field theories.
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