SciPost Submission Page
Quantum Groups as Global Symmetries II. Coulomb Gas Construction
by Barak Gabai, Victor Gorbenko, Jiaxin Qiao, Bernardo Zan, Aleksandr Zhabin
Submission summary
| Authors (as registered SciPost users): | Jiaxin Qiao · Aleksandr Zhabin |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2410.24143v4 (pdf) |
| Date accepted: | Aug. 25, 2025 |
| Date submitted: | Aug. 16, 2025, 5:51 p.m. |
| Submitted by: | Aleksandr Zhabin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We study a conformal field theory that arises in the infinite-volume limit of a spin chain with $U_q(sl_2)$ global symmetry. Most operators in the theory are defect-ending operators which allows $U_q(sl_2)$ symmetry transformations to act on them in a consistent way. We use Coulomb gas techniques to construct correlation functions and compute all OPE coefficients of the model, as well as to prove that the properties imposed by the quantum group symmetry are indeed satisfied by the correlation functions. In particular, we treat the non-chiral operators present in the theory. Free boson realization elucidates the origin of the defects attached to the operators. We also comment on the role of quantum group in generalized minimal 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
Author comments upon resubmission
List of changes
Addressing the comments of the referee report 2, we have made the following improvements to the paper:
-
A sentence about the existence of stress-energy tensor and locality of CFT was added in the introduction.
-
A phrase
as well as some additional defect lines'' was replaced with a phraseand topological defect lines coming from free boson CFT'' in the last paragraph of the introduction. The aim of this paragraph is to briefly announce the construction of section 3.2. We hope this would be enough for the introduction. -
Phrasing changed.
-
Notation added.
-
The word ``torus'' referring to partition function was removed.
6-7. We thank the referee for pointing out the subtleties with operators $\mathcal{V}_\alpha$ and $\mathcal{V}_{2\alpha_0-\alpha}$. A paragraph after eq. (3.12) was modified as well as the paragraph in the end of section 3.2.1 was added. The reference to section 4.1 was also added. We hope this discussion is now made more clear.
-
A phrase in the description of figure 4 was added, emphasizing that dashed lines can cross contours.
-
Typo corrected.
-
Phrasing changed.
-
Typo corrected.
-
More explanation of figure 22 was added.
-
Mentioning of reference [3] was added.
-
Typo corrected.
-
We thank the referee for suggestion of changing the notation of $x_k, x_{k+1}$. However, we believe that the notation we chose is consistent, and moreover changing the notation in the entire section at this point can lead to additional typos. We hope the referee agrees to keep the notation as it is.
16-21. Typos corrected.
Published as SciPost Phys. 19, 070 (2025)