SciPost Submission Page
Non-Invertible Anyon Condensation and Level-Rank Dualities
by Clay Cordova, Diego García-Sepúlveda
Submission summary
| Authors (as registered SciPost users): | Diego Garcia-Sepulveda |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2312.16317v1 (pdf) |
| Date submitted: | 2024-05-03 21:40 |
| Submitted by: | Garcia-Sepulveda, Diego |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We derive new dualities of topological quantum field theories in three spacetime dimensions that generalize the familiar level-rank dualities of Chern-Simons gauge theories. The key ingredient in these dualities is non-abelian anyon condensation, which is a gauging operation for topological lines with non-group-like i.e. non-invertible fusion rules. We find that, generically, dualities involve such non-invertible anyon condensation and that this unifies a variety of exceptional phenomena in topological field theories and their associated boundary rational conformal field theories, including conformal embeddings, and Maverick cosets (those where standard algorithms for constructing a coset model fail.) We illustrate our discussion in a variety of isolated examples as well as new infinite series of dualities involving non-abelian anyon condensation including: i) a new description of the parafermion theory as $(SU(N)_{2} \times Spin(N)_{-4})/\mathcal{A}_{N},$ ii) a new presentation of a series of points on the orbifold branch of $c=1$ conformal field theories as $(Spin(2N)_{2} \times Spin(N)_{-2} \times Spin(N)_{-2})/\mathcal{B}_{N}$, and iii) a new dual form of $SU(2)_{N}$ as $(USp(2N)_{1} \times SO(N)_{-4})/\mathcal{C}_{N}$ arising from conformal embeddings, where $\mathcal{A}_{N}, \mathcal{B}_{N},$ and $\mathcal{C}_{N}$ are appropriate collections of gauged non-invertible bosons.
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
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The paper uses anyon condensation in 3d Chern-Simons gauge theories to identify and conjecture new dualities that generalize the more familiar level-ranking dualities by including non-invertible 1-form gaugings. Such dualities are also closely related to various equivalent descriptions of 2d rational conformal field theories (including the so-called Maverick cosets) which the authors explain in detail. The authors include many examples with explicit details which are useful for the readers learning the subject. The paper is clear and well-written and I think should be published after the following suggestions are taken into consideration.
Requested changes
1. the authors might want to briefly comment on their results in relation to Witt group/Witt equivalence
2. it would be useful if the authors can give some general characterization on the condensable anyons A_k in (1.13) and B_N in (1.16) and A_{N,k} in (1.22), to make these conjectures more meaningful/useful, in addition to the examples at small N,k.
3. obvious typos: SU(1)1 in (1.28) and also above (3.20)
4. obvious typo in footnote 10
5. the authors should clarify whether condition 3) above Sec 4.1 is necessary and sufficient for anyons to be confined/deconfined
6. typo in first eqn of (4.17)
7. I got a bit lost with Sec 5.2.2. It's well-known that SO(3)4 is Fib^2 and (G2)_1 is \bar Fib and the claimed duality follows immediately. The authors may intended to use this as a pedagogical example to illustrate the procedure? But since the procedure is elementary and already illustrated at length in previous sections perhaps this can be moved to an appendix?
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report
1. The paper uses the modern understanding of non-invertible symmetries and their gauging to unify various constructions of 2d CFTs.
2. The paper highlights certain exceptional cases in the GKO coset construction where the procedure to obtain a CFT with a single vacuum by gauging a centre symmetry fails. The authors show that such cases and Maverick cosets can be unified with the usual coset construction through the gauging of certain non-invertible symmetry of the bulk TQFT.
3. While, in general, gauging non-invertible symmetries is complicated, in the several examples considered in the paper, the authors cleverly use various consistency conditions to identify the set of non-invertible line operators that can be gauged. The authors also use other consistency conditions to obtain the details of the theory after gauging.
4. The authors highlight that when the chiral algebra of a 2d CFT has two different descriptions, it can be used to obtain two different descriptions of the same modular tensor category, leading to a duality. Using various conformal embeddings and associated anyon condensations, the authors derive several new dualities between 2+1d TQFTs.
5. The journal acceptance criteria 4 which requires that the article contain a conclusion with a summary of results is not met. However, the paper contains a very clear summary of the main results in the introduction.
The paper is well-written and clear. Modulo some minor corrections/suggestions below, I strongly recommend it for publication in SciPost.
Requested changes
1. Page 4, paragraph 2, typo in line 1: ‘a treatment non-invertible’.
2. Page 56: The discussion of unitary MTC is slightly confusing. The authors may want to emphasize that having a unitary S-matrix does not imply that the MTC is unitary. Unitarity of the MTC requires (among others)
a. Positive quantum dimensions.
b. A basis in which the F matrices are unitary.
In particular, these conditions are crucial to conclude that $d_a=1 \implies$ $a \times \bar a =1$ . For example, see https://arxiv.org/abs/1209.2022.
3. The authors use the term ‘Lagrangian algebra’ in several places in the bulk of the paper. Since the term is defined in Appendix B, it may be useful if the authors point the reader to this Appendix when the term is first used in the paper.
Recommendation
Ask for minor revision