SciPost Submission Page
Integrable Deformations from Twistor Space
by Lewis T. Cole, Ryan A. Cullinan, Ben Hoare, Joaquin Liniado, Daniel C. Thompson
Submission summary
| Authors (as registered SciPost users): | Lewis Cole · Joaquin Liniado |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202404_00042v1 (pdf) |
| Date submitted: | 2024-04-25 23:35 |
| Submitted by: | Liniado, Joaquin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons in 6 dimensions. We provide the first complete description of this diamond of integrable theories for a family of deformed sigma models, going beyond the Dirichlet boundary conditions that have been considered thus far. Starting from 6d holomorphic Chern-Simons theory on twistor space with a particular meromorphic 3-form $\Omega$, we construct the defect theory to find a novel 4d integrable field theory, whose equations of motion can be recast as the 4d anti-self-dual Yang-Mills equations. Symmetry reducing, we find a multi-parameter 2d integrable model, which specialises to the $\lambda$-deformation at a certain point in parameter space. The same model is recovered by first symmetry reducing, to give 4d Chern-Simons with generalised boundary conditions, and then constructing the defect theory.
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
Author comments upon resubmission
With kind regards,
Lewis Cole, Ryan Cullinan, Ben Hoare, Joaquin Liniado & Daniel Thompson
List of changes
Report 1
Main questions
• 1 - We agree that in section 6 the correct definition is h = (h, ˜h). The rest of the E-model
formulation was correspondingly amended.
• 2 - We have redone the calculation in appendix B with the correct factor of ⟨πβ⟩ in the numerator
as pointed out by the referee. As expected, the final action is the same, but the intermediate steps
are altered.
Minor changes
• 2 to 6 - Corrected.
• 7 - Changed sign in eq. (4.10) and clarified CS4 conventions to ensure signs are consistent throughout.
• 8 to 12 - Corrected.
• 13 - Added definition of cG.
• 14 - Corrected.
• 15 - We have added explicit expressions in a coordinate basis for Ji in appendix A.3, for which
J1J2J3 = +id. This specification is correlated to the stated Kähler forms being self-dual and our
field theory being ASDYM with our choice of orientation, as opposed to the other way round.
• 16 - Amended.
• 17 - Added footnote 10.
• 18 - Amended.
• 19 - Added footnote 12.
• 20 - Added comment.
• 21 - Amended.
Report 2
• 1 - We agree that this is an important subtlety that is not fully resolved. After some initial
investigations we believe that a more thorough analysis is required and have left it as an open
question. We have added a paragraph highlighting this point below eq.(3.46).
• 2 - Added comment.
• 3 - The referee’s comment motivated us to look in more detail at reality conditions and their
twistorial origin. Our original approach was direct inspection of the 4d IFT. We have retained
this analysis in section 3.3, but we have rewritten it to make the key points clearer and to better
prepare for a discussion from the perspective 6d hCS and twistors, which we have added after. This
highlighted one new reality condition, which we have also included.
• 4 and 5 - Amended.