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Continuous Family of Conformal Field Theories and Exactly Marginal Operators.
Shota Komatsu1, Yuya Kusuki2,3,4, Marco Meineri5
1CERN, Department of Theoretical Physics, 1211 Meyrin, Switzerland.
Physical Review Letters
|July 7, 2026
Summary
A conformal manifold implies exactly marginal operators, provided a conformal interface exists. This operator, crucial for connecting conformal field theories, can be reconstructed from the interface displacement operator, independent of specific models.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
Background:
- Conformal field theories (CFTs) are fundamental in various areas of physics.
- The existence and properties of exactly marginal operators are key to understanding CFTs and their deformations.
- The relationship between conformal manifolds and exactly marginal operators remains an open question.
Purpose of the Study:
- To determine if a conformal manifold necessitates the existence of exactly marginal operators.
- To provide a method for constructing such operators.
- To establish a model-independent connection between conformal interfaces and marginal operators.
Main Methods:
- The study assumes the existence of a conformal interface with specific properties connecting nearby CFTs.
- It utilizes the general principles of conformal symmetry.
- The construction relies on the interface displacement operator.
Main Results:
- The existence of a conformal manifold implies the existence of exactly marginal operators.
- A method is presented to reconstruct the exactly marginal operator from the interface displacement operator.
- The construction is demonstrated to be model-independent.
Conclusions:
- The affirmative answer to the central question provides a significant theoretical link.
- The developed construction offers a general tool for identifying and utilizing exactly marginal operators.
- This work deepens the understanding of conformal symmetry and its implications for quantum field theories.
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