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Non-invertible symmetries of two-dimensional Non-Linear Sigma Models
by Guillermo Arias-Tamargo, Chris Hull, Maxwell L. Velásquez Cotini Hutt
Submission summary
| Authors (as registered SciPost users): | Guillermo Arias-Tamargo · Maxwell L. Velásquez Cotini Hutt |
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| Preprint Link: | scipost_202510_00003v1 (pdf) |
| Date accepted: | Oct. 21, 2025 |
| Date submitted: | Oct. 3, 2025, 5 p.m. |
| Submitted by: | Guillermo Arias-Tamargo |
| Submitted to: | SciPost Physics |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
Global symmetries can be generalised to transformations generated by topological operators, including cases in which the topological operator does not have an inverse. A family of such topological operators are intimately related to dualities via the procedure of half-space gauging. In this work we discuss the construction of non-invertible defects based on T-duality in two dimensions, generalising the well-known case of the free compact boson to any Non-Linear Sigma Model with Wess-Zumino term which is T-dualisable. This requires that the target space has an isometry with compact orbits that acts without fixed points. Our approach allows us to include target spaces without non-trivial 1-cycles, does not require the NLSM to be conformal, and when it is conformal it does not need to be rational; moreover, it highlights the microscopic origin of the topological terms that are responsible for the non-invertibility of the defect. An interesting class of examples are Wess-Zumino-Witten models, which are self-dual under a discrete gauging of a subgroup of the isometry symmetry and so host a topological defect line with Tambara-Yamagami fusion. Along the way, we discuss how the usual 0-form symmetries match across T-dual models in target spaces without 1-cycles, and how global obstructions can prevent locally conserved currents from giving rise to topological operators.
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Author comments upon resubmission
We wish to thank the referee for their careful reading of the draft and their comments. We have addressed them as follows:
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We have included a new paragraph at the end of the introduction in page 5 explaining how, once the discrete gauge fields have been integrated out and the self-duality conditions are satisfied, the defect becomes localised to \gamma and can be inserted on any cycle of the worldsheet, not necesarily trivial. We have not changed the paragraph in page 4 as, a priori, the requirement on gamma to be trivial is necesary for the half space gauging.
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We have rephrased that paragraph at the end of section two. The point we wish to make is that there are two ways of proceeding with the discrete gauging, one as an orbifold and another via introducing background gauge fields and integrating them out. These do not lead to the same lagrangian, but they lead to the same quantum theory thanks to T duality.
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We have corrected the typo in eq. (4.20), and thank the referee for spotting it.
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We agree with the point of the referee and have removed this paragraph.
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We have modified the paragraph discussing the implications of the symmetry in non conformal NLSMs. It turns out that in sigma models that have the symmetry in the UV, the beta function for the relevant coupling does vanish; however, we felt this point was interesting enough on its own, and have written a manuscript that appeared on the arxiv last week. We thank the referee for the suggestion of the 1-loop computation. It can also happen that the symmetry is emergent in the IR, e.g. for a generic sigma model flowing to a WZW model.
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The question of mirror symmetry is very interesting, and we share the intuition that there should be a self-duality defect associated to self mirror pairs (or a suitable generalisation that includes the discrete gauging). However there seems to be an obstacle. To the best of our knowledge, the proof of mirror symmetry for 2d SCFTs relates a CY sigma model to a mirror LG model. Via the CY-LG correspondence, this then corresponds to the mirror CY sigma model. However, this correspondence requires the tuning of an FI parameter of a gauged linear sigma model from positive to negative values. It is not clear at all to us how this tuning can be achieved by a "topological manipulation" of some form, and as a consequence, we do not see at present how a half-space-gauging-like procedure will lead to a topological defect where the theory on both sides is the same thanks to mirror symmetry.
Best regards, the authors.
Published as SciPost Phys. 19, 126 (2025)