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Parisi-Sourlas Supertranslation and Scale Invariance without Conformal Symmetry
1Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-Ku, Kyoto 606-8502, Japan.
Physical Review Letters
|April 18, 2025
Summary
This study explores a field theory with Parisi-Sourlas supertranslation symmetry, finding nine scale-invariant points, but only one is conformal. It explains the nonrenormalization of the virial current via supercurrent relation.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- Supersymmetry
Background:
- Emergent supersymmetry in critical random systems.
- Field theory with quartic potential and Parisi-Sourlas supertranslation symmetry.
Purpose of the Study:
- Investigate scale-invariant renormalization group fixed points.
- Clarify the existence and properties of the virial current.
- Understand the relationship between scale invariance and conformal invariance.
Main Methods:
- Perturbative epsilon expansion.
- Analysis of renormalization group fixed points.
- Ward-Takahashi identity for supertranslation.
Main Results:
- Identified nine nontrivial scale-invariant fixed points.
- Only one fixed point exhibits conformal invariance.
- Demonstrated the virial current's relation to the supercurrent.
- Explained the nonrenormalization of the virial current.
Conclusions:
- Scale invariance without conformal invariance is nongeneric without specific mechanisms.
- Supertranslation symmetry and Ward-Takahashi identities are crucial for understanding nonrenormalized operators.
- The model provides insights into emergent supersymmetry and critical phenomena.
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