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Orbifolds of chiral fermionic CFTs and their duality
by Kohki Kawabata, Shinichiro Yahagi
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Submission summary
| Authors (as registered SciPost users): | Kohki Kawabata · Shinichiro Yahagi |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202410_00017v1 (pdf) |
| Date submitted: | 2024-10-11 07:51 |
| Submitted by: | Kawabata, Kohki |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We consider chiral fermionic conformal field theories (CFTs) constructed from lattices and investigate their orbifolds under reflection and shift Z2 symmetries. For lattices based on binary error-correcting codes, we show the duality between reflection and shift orbifolds using a triality structure inherited from the binary codes. Additionally, we systematically compute the partition functions of the orbifold theories for both binary and nonbinary codes. Finally, we explore applications of this code-based construction in the search for supersymmetric CFTs and chiral fermionic CFTs without continuous symmetries.
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
Current status:
Reports on this Submission
Report
The manuscript under review studies chiral fermionic theories with a Z2 symmetry in addition to the conventional fermion parity symmetry. The authors systematically analyze various Z2 gauging.
The authors expand the known correspondence between error-correcting codes and CFTs into the fermionic cases. They also provides an equivalence between different orbifolds, pointing to a deeper symmetry structure in code-based CFTs.
A key result is to demonstrate a duality between reflection and shift orbifolds for theories built from binary codes, utilizing a triality symmetry between the the SU(2) current algebras, which is nobel and original.
They also present the explicit computation of orbifold partition functions from code invariants, which is original and highly practical. This approach allows for an efficient classification of fermionic CFTs derived from code-based lattices.
The manuscript is well-written and presents interesting and new results. Thus, it will easily pass the criteria to be published in this journal, once a few minor questions are properly addressed:
(1) The duality between T/G and T/H is established under the assumption of a binary code construction, where triality relies on the presence of three SU(2) currents from weight-2 codewords. The reviewer wonders whether such an argument can be generalized to non-binary code CFTs.
(2) In Section 7.5, the authors constructed two theories with a spectral gap greater than 1. The reviewer is curious whether these theories are associated with certain sporadic finite groups.
Recommendation
Ask for minor revision
Strengths
1- Carefully written manuscript
2- Connections with recent classification on c=16 chiral fermionic CFTs
3- Opens a way to construct new chiral CFTs with moderately large values of c, thanks to the code construction
Weaknesses
1- Many technical details that could have been moved to an appendix
Report
This paper considers chiral fermionic CFTs constructed from lattices and error-correcting codes, and various operations on them. The main result is the equivalence of two orbifolds, by reflection and by shift. It also discusses the relation to explicit examples of chiral fermionic CFTs code constructions over Z_2 and general Z_k. This leads to a reproduction of the CFTs from the recent classification at c=16.
Here is some general skepticism: There is a growing literature on explicit constructions of chiral CFTs from lattices/codes, often heavy with details and without a clear physical motivation. In this paper, however, the authors manage to convey an appealing motivation for this work. Apart from the result on the equivalence of orbifold constructions, a great merit of the paper is section 7 which presents an array of interesting examples relating to both known and new CFTs.
The paper is well-written and the main results are summarised in the introduction. The results are interesting and the paper deserves to be published. The presentation could have benefited from moving some material into an appendix, but I accept the authors' choice to keep all information in the main text. I recommend publishing as submitted.
Requested changes
Typo: page 10: fermion party -> fermion parity
Recommendation
Publish (meets expectations and criteria for this Journal)
Author: Kohki Kawabata on 2025-04-17 [id 5385]
(in reply to Report 2 on 2025-02-27)Thank you very much for reviewing our manuscript. We address the questions raised by the referee as follows:
(1) In the binary construction, the SU(2) current is always present in the spectrum due to the structure of Construction A. However, in the non-binary case, the presence of a current depends on the specific code used in constructing the CFT. Therefore, the duality that holds in the binary setting cannot be straightforwardly generalized to the non-binary case.
(2) When the spectral gap exceeds 1, the theory does not exhibit any continuous symmetry but is expected to possess some discrete symmetry. At present, we have not yet identified these discrete symmetries, but it would be interesting to investigate their possible relation to the symmetries of the underlying code.