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Non-Invertible T-duality at Any Radius via Non-Compact SymTFT
by Riccardo Argurio, Andrés Collinucci, Giovanni Galati, Ondrej Hulik, Elise Paznokas
Submission summary
| Authors (as registered SciPost users): | Riccardo Argurio · Giovanni Galati |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2409.11822v1 (pdf) |
| Date submitted: | 2024-10-21 14:59 |
| Submitted by: | Argurio, Riccardo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We extend the construction of the T-duality symmetry for the 2d compact boson to arbitrary values of the radius by including topological manipulations such as gauging continuous symmetries with flat connections. We show that the entire circle branch of the $c=1$ conformal manifold can be generated using these manipulations, resulting in a non-invertible T-duality symmetry when the gauging sends the radius to its inverse value. Using the recently proposed symmetry TFT describing continuous global symmetries of the boundary theory, we identify the topological operator corresponding to these new T-duality symmetries as an open condensation defect of the bulk theory, constructed by (higher) gauging an $\mathbb{R}$ subgroup of the bulk global symmetries. Notably, when the boundary theory is the compact boson with a rational square radius, this operator reduces to the familiar T-duality defect described by a Tambara-Yamagami fusion category. This construction thus naturally includes all possible discrete T-duality symmetries of the theory in a unified way.
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This paper provides a clear and explicit discussion of T duality symmetry in the 2d compact boson from a symmetry TFT perspective, identifying the T duality symmetry defect with an open condensation defect of the bulk theory. It gives a nice application of the recent work on symmetry TFT for continuous symmetries. I recommend this paper for publication, though I would like the authors to answer/comment on the following:
1) Can you compare/contrast the approach here for mapping between boundary defects and bulk condensation defects to the non-flat gauging in [28]?
2) Under Eq 4.1, why does this set the normalization "more generally"? A condensation defect can also annihilate lines entirely. Maybe you need it to map at least the trivial line to the trivial line with unit prefactor?
2) What would the integral i.e. in eq 4.2 mean for a concrete operator acting on the Hilbert space in a lattice model?
3) Would there be subtleties with the T duality symmetry defect seeming to have infinite quantum dimension?
4) In a Tambara-Yamagami fusion category there is also a choice of symmetric bicharacter (which in this simple example may be fixed) and Frobenius-Schur indicator. Perhaps you can mention how to incorporate especially the latter piece of data into the symmetry TFT.
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