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Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
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Parisi-Sourlas Supersymmetry in Random Field Models
Apratim Kaviraj1,2,3, Slava Rychkov2,4, Emilio Trevisani2,5
1Institut de Physique Théorique Philippe Meyer, ENS, Université PSL, CNRS Sorbonne Université, Université de Paris, F-75005 Paris, France.
Physical Review Letters
|August 8, 2022
Summary
The Parisi-Sourlas conjecture suggests a supersymmetric conformal field theory (CFT) describes random field disorder critical points. This study explains why this CFT is not reached for certain models due to new SUSY-breaking interactions.
Area of Science:
- Condensed Matter Physics
- High Energy Physics
- Statistical Mechanics
Background:
- The Parisi-Sourlas conjecture posits a connection between random field (RF) disorder critical points and supersymmetric (SUSY) conformal field theories (CFTs).
- Numerical studies support this for the RF $\phi^3$ model but not the RF $\phi^4$ model in dimensions below 5.
Purpose of the Study:
- To investigate why the predicted SUSY fixed point is not attained in the RF $\phi^4$ model.
- To identify the mechanisms preventing the realization of the conjectured SUSY CFT.
Main Methods:
- Utilizing a perturbative renormalization group approach.
- Employing a carefully selected field basis for systematic interaction analysis.
Main Results:
- Identified new relevant SUSY-breaking interactions as the cause for not reaching the SUSY fixed point.
- Developed a method to systematically explore the interaction space.
Conclusions:
- The findings explain the discrepancy between the Parisi-Sourlas conjecture and numerical results for the RF $\phi^4$ model.
- The perturbative renormalization group calculations align with existing numerical data for both cubic and quartic potentials.
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