Braided Zesting and Its Applications

Delaney, Colleen; Galíndo, César; Plavnik, Julia Yael; Rowell, Eric C.; Zhang, Qing

doi:10.1007/s00220-021-04002-4

Cited by 17 publications

(55 citation statements)

References 23 publications

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“…It is known that for non-trivial α and its inverse we get the MTC SU(3) 3 and its complex conjugate under gauging [74]. SU(3) 3 has only one non-trivial Galois conjugate [91], which is the complex conjugate of SU(3) 3 . Therefore, Galois conjugation of the electric theory corresponds to changing the Z 3 -SPT being stacked before gauging (α → ᾱ).…”

Section: -Fermion Model With Z 3 Symmetrymentioning

confidence: 99%

“…Therefore, the electric theory obtained for trivial α is in fact completely Galois invariant. Indeed, one can check that the modular data for this theory given in [91] is invariant under Galois conjugation (up to permutation of the anyons). This is an example of a Galois invariant non-abelian TQFT which is not a discrete gauge theory.…”

Section: -Fermion Model With Z 3 Symmetrymentioning

confidence: 99%

“…• Another interesting operation which takes us between TQFTs is Zesting [91]. Like Galois conjugation, zesting can be used to find modular isotopes [92].…”

Section: Jhep01(2022)004 6 Conclusionmentioning

confidence: 99%

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Galois orbits of TQFTs: symmetries and unitarity

Buican

Radhakrishnan

2022

J. High Energ. Phys.

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We study Galois actions on 2+1D topological quantum field theories (TQFTs), characterizing their interplay with theory factorization, gauging, the structure of gapped boundaries and dualities, 0-form symmetries, 1-form symmetries, and 2-groups. In order to gain a better physical understanding of Galois actions, we prove sufficient conditions for the preservation of unitarity. We then map out the Galois orbits of various classes of unitary TQFTs. The simplest such orbits are trivial (e.g., as in various theories of physical interest like the Toric Code, Double Semion, and 3-Fermion Model), and we refer to such theories as unitary “Galois fixed point TQFTs”. Starting from these fixed point theories, we study conditions for preservation of Galois invariance under gauging 0-form and 1-form symmetries (as well as under more general anyon condensation). Assuming a conjecture in the literature, we prove that all unitary Galois fixed point TQFTs can be engineered by gauging 0-form symmetries of theories built from Deligne products of certain abelian TQFTs.

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Section: -Fermion Model With Z 3 Symmetrymentioning

confidence: 99%

Section: -Fermion Model With Z 3 Symmetrymentioning

confidence: 99%

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Galois orbits of TQFTs: symmetries and unitarity

Buican

Radhakrishnan

2022

J. High Energ. Phys.

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“…We present the details of zesting here. The case of zesting spin modular categories by the sVec subcategory afforded by the distinguished fermion is worked out in [3], and the general case is found in [8].…”

Section: Zesting To Realize Casementioning

confidence: 99%

On Realizing Modular Data

Bonderson,

Rowell,

Wang

2019

Preprint

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“…The pentagon and hexagon axioms constrain ω and χ significantly-for example, if |G| is odd then the only abelian 3-cocycles have ω trivial. This can be regarded as a special case of (braided) zesting introduced in [5].…”

Section: Introductionmentioning

confidence: 99%

Reconstructing Braided Subcategories of $SU(N)_k$

Feng¹,

Rowell²,

Ming³

2022

Preprint

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Ocneanu rigidity implies that there are finitely many (braided) fusion categories with a given set of fusion rules. While there is no method for determining all such categories up to equivalence, there are a few cases for which can. For example, Kazhdan and Wenzl described all fusion categories with fusion rules isomorphic to those of SU (N ) k . In this paper we extend their results to a statement about braided fusion categories, and obtain similar results for certain subcategories of SU (N ) k .

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Braided Zesting and Its Applications

Cited by 17 publications

References 23 publications

Galois orbits of TQFTs: symmetries and unitarity

Galois orbits of TQFTs: symmetries and unitarity

On Realizing Modular Data

Reconstructing Braided Subcategories of $SU(N)_k$

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