SciPost Submission Page
Orthogonality of Q-Functions up to Wrapping in Planar N = 4 Super Yang–Mills Theory
by Till Bargheer, Carlos Bercini, Andrea Cavaglià, Davide Lai, Paul Ryan
Submission summary
| Authors (as registered SciPost users): | Till Bargheer · Paul Ryan |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00077v2 (pdf) |
| Date submitted: | Nov. 18, 2025, 7:12 a.m. |
| Submitted by: | Paul Ryan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We construct orthogonality relations in the Separation of Variables framework for the sl(2) sector of planar N = 4 supersymmetric Yang–Mills theory. Specifically, we find simple universal measures that make Q-functions of operators with different spins vanish at all orders in perturbation theory, prior to wrapping corrections. To analyze this rank-one sector, we relax some of the assumptions thus far considered in the Separation of Variables framework. Our findings may serve as guidelines for extending this formalism to other sectors of the theory as well as other integrable models.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
- As requested by one of the referees, we highlighted the importance of two papers already cited ([21],[22] in the new labeling). In the introduction we changed
"... the Separation of Variables (SoV) method, which was pioneered by Sklyanin [20] and has undergone rapid advancement in recent years ..." to "the Separation of Variables (SoV) method, which was pioneered by Sklyanin [20] and extensively developed in sl(2)-based models in [21, 22]. The formalism has undergone rapid advancement in recent years ..."
- Added a new sentence to the Acknowledgements.
- Minor grammar / spelling / reformulation of one or two sentences.
- Added a few additional references.
Current status:
Reports on this Submission
Report
These new SoV-type expressions are twist-independent and generalisable to higher orders and different twists, although they currently do not account for degeneracies among states with equal spin.
However, the proposed multiple integral is not yet a scalar product, because at each order it gives different normalisation factors when compared to the Gaudin norm.
Another problem is that the proposed expression does not vanish when the two
Q-functions have the same spin but different other charges.
The authors discuss several possible ways to resolve these issues.
I think that the this results of this paper, although partial, might give insights
about how to develop the SoV approach to the N=4 SYM for finite coupling.
I recommend publication
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
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the paper makes progress in a field where progress has been very slow
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it cures some of the problems of the previous, three-year old attempt to solve the problem
Weaknesses
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the method provided doesn't work for states with degenerate spin that should be orthogonal
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a clear overall picture is still to emerge
Report
Requested changes
None
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)