What the study found
Yangian symmetry, a kind of symmetry in some mathematical physics models, is classically realized in the bi-scalar and supersymmetric fishnet models when specific evaluation parameter patterns are used. The authors also report that this symmetry does not extend to generic quantum correlation functions in the bi-scalar model beyond previously known classes of Yangian-invariant correlators.
Why the authors say this matters
The authors conclude that their findings point to a connection between the failure of quantum Yangian symmetry and a non-zero dual Coxeter number, a mathematical property of the symmetry algebra. They say this may also be relevant to complete integrability in planar quantum field theory models.
What the researchers tested
The researchers investigated Yangian symmetry for the equations of motion and the action of the classical bi-scalar and supersymmetric fishnet models in four spacetime dimensions. They then discussed whether the symmetry applies to planar correlation functions.
What worked and what didn't
The symmetry was found to be classically realized in these models under specific evaluation parameter patterns. However, the authors present several counter-examples showing that generic quantum correlation functions in the bi-scalar model are not Yangian invariant, including correlators given by sums of Feynman graphs and bi-scalar graphs with octagon-shaped loops.
What to keep in mind
The abstract describes explicit counter-examples and notes that the results apply to the bi-scalar model beyond already established classes of Yangian-invariant correlators. It also indicates that the discussion is about classical versus quantum behavior in four spacetime dimensions, and it does not provide further limitations in the available summary.
Key points
- Yangian symmetry is classically realized in the bi-scalar and supersymmetric fishnet models under specific evaluation parameter patterns.
- Generic quantum correlation functions in the bi-scalar model are not Yangian invariant, according to the authors.
- The paper gives counter-examples involving sums of Feynman graphs and octagon-shaped loop graphs.
- The authors say a non-zero dual Coxeter number may be an obstacle to quantum Yangian symmetry.
- They suggest this may also matter for complete integrability in planar quantum field theory models.
Disclosure
- Research title:
- Yangian symmetry is classical but not generic in fishnet models
- Image credit:
- Photo by Merlin Lightpainting on Pexels
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