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Main Authors: Jeong, Kibok, Lee, Soochang
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2511.16380
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author Jeong, Kibok
Lee, Soochang
author_facet Jeong, Kibok
Lee, Soochang
contents We propose a field theoretic realization of the non-unitary $\mathfrak{sl}(2,\mathbb{C})$ Witten-Reshetikhin-Turaev Topological Quantum Field Theory(WRT TQFT). The WRT TQFT at the principal root of unity is unitary. It is known to be realized by $\mathrm{SU}(2)$ Chern-Simons theory. However, the WRT TQFT at a non-principal root of unity is non-unitary. Its field theoretic realization has remained unclear. We propose that such a non-unitary TQFT arises from the topological twist of the 3-dimensional $\mathcal{N}=4$ rank-0 theory constructed by joining multiple $T[\mathrm{SU}(2)]$ theories. We construct its modular matrices and identify them with those of the WRT TQFT, establishing a concrete relation between the parameters, up to a decoupled unitary TQFT.
format Preprint
id arxiv_https___arxiv_org_abs_2511_16380
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle QFT Realization of Non-Unitary $\mathfrak{sl}(2,\mathbb{C})$ WRT Invariants and Their Galois Conjugations
Jeong, Kibok
Lee, Soochang
High Energy Physics - Theory
We propose a field theoretic realization of the non-unitary $\mathfrak{sl}(2,\mathbb{C})$ Witten-Reshetikhin-Turaev Topological Quantum Field Theory(WRT TQFT). The WRT TQFT at the principal root of unity is unitary. It is known to be realized by $\mathrm{SU}(2)$ Chern-Simons theory. However, the WRT TQFT at a non-principal root of unity is non-unitary. Its field theoretic realization has remained unclear. We propose that such a non-unitary TQFT arises from the topological twist of the 3-dimensional $\mathcal{N}=4$ rank-0 theory constructed by joining multiple $T[\mathrm{SU}(2)]$ theories. We construct its modular matrices and identify them with those of the WRT TQFT, establishing a concrete relation between the parameters, up to a decoupled unitary TQFT.
title QFT Realization of Non-Unitary $\mathfrak{sl}(2,\mathbb{C})$ WRT Invariants and Their Galois Conjugations
topic High Energy Physics - Theory
url https://arxiv.org/abs/2511.16380