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Do Drinfeld twists of $AdS_5 \times S^5$ survive light-cone quantization?
by Stijn J. van Tongeren, Yannik Zimmermann
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Submission summary
| Authors (as registered SciPost users): | Yannik Zimmermann |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2112.10279v1 (pdf) |
| Date submitted: | 2022-01-14 14:40 |
| Submitted by: | Zimmermann, Yannik |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study how a wide class of Abelian Yang-Baxter deformations of the $AdS_5 \times S^5$ string behave at the quantum level. These deformations are equivalent to TsT transformations and conjectured to be dual to beta, dipole, and noncommutative deformations of SYM. Classically they correspond to Drinfeld twists of the original theory. To verify this expectation at the quantum level we compute and match (1) the bosonic two-body tree-level worldsheet scattering matrix of these deformations in the uniform light-cone gauge, and (2) the Bethe equations of the equivalent model with twisted boundary conditions. We find that for a generalization of gamma deformations of the BMN string the we are able to express the S matrix either through a Drinfeld twist or a shift of momenta. For deformations of the GKP string around the null-cusp solution we encounter calculational obstacles that prevent us from calculating the scattering matrix.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2022-3-15 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2112.10279v1, delivered 2022-03-15, doi: 10.21468/SciPost.Report.4687
Report
This paper deals with simple integrable deformations of the AdS5xS5 string of Yang-Baxter type. In particular it considers abelian deformations involving the Cartan directions, which are equivalent to TsT transformations. It is expected that these deformations should be captured by Drinfeld twists of the undeformed S-matrix. The authors verify this by comparing the twisted S-matrix for a BMN string to the tree-level 2-particle S-matrix found from the deformed Lagrangian and showing that they agree. The exception to this is when the deformation involves the light-cone directions used in the gauge fixing. Here the deformation acts instead by a shift in the momenta. They also attempt to analyse the GKP string, but in that case they are not able to find a gauge that allows for a perturbative treatment.
The paper is clearly written and the results are interesting, though not unexpected. The situation for the GKP string is somewhat unsatisfactory, in that it is not clear whether the problem they encounter is simply a technical one that could be easily overcome. Nevertheless, I feel that the paper is interesting and novel enough to warrant publication in SciPost.