Galois conjugation and multiboundary entanglement entropy

Buican, Matthew; Radhakrishnan, Rajath

doi:10.1007/jhep12(2020)045

Cited by 9 publications

(9 citation statements)

References 50 publications

(146 reference statements)

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“…These results, along with our earlier work [24], show that, while Galois conjugation usually results in distinct TQFTs, the TQFTs in a Galois orbit are closely related to each other. They have the same symmetry structure (modulo mild assumptions in the defining number field of the G-crossed braided theory), and their gapped boundaries are related to each other.…”

Section: Jhep01(2022)004 6 Conclusionsupporting

confidence: 81%

“…H, then it can be seen as a discrete gauge theory based on the gauge group G or the gauge group H. That is, the gauge group is not duality invariant. 24 Therefore, Galois invariance of the gauge group of the discrete gauge theory is more precisely stated as follows: Given a discrete gauge theory Z(Vec ω G ), all of its Galois conjugates are G gauge theories up to dualities. In fact, the dualities of a discrete gauge theory are determined by the Lagrangian subcategories in the theory and they have been classified in [54,55].…”

Section: Jhep01(2022)004mentioning

confidence: 99%

“…Therefore Galois conjugate TQFTs are typically not dual theories. Still, one can define quantities like multi-boundary entanglement entropy, which are invariant under Galois conjugation in abelian TQFTs, and in an infinite set of links in non-abelian TQFTs [24].…”

Section: Introductionmentioning

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: Jhep01(2022)004 6 Conclusionsupporting

confidence: 81%

Section: Jhep01(2022)004mentioning

confidence: 99%

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Galois orbits of TQFTs: symmetries and unitarity

Buican

Radhakrishnan

2022

J. High Energ. Phys.

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“…The topological entanglement structure can be obtained by tracing out one of the boundary components, which is often termed as 'multi-boundary entanglement'. We refer the interested readers to [5][6][7][8][9][10][11][12][13][14][15] for the recent developments in this study. For the three-manifold M whose boundary consists of multiple disjoint torus boundaries (∂M = Σ 1 Σ 2 .…”

Section: Jhep10(2021)172mentioning

confidence: 99%

Topological entanglement and hyperbolic volume

Dwivedi

Mandal

et al. 2021

J. High Energ. Phys.

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The entanglement entropy of many quantum systems is difficult to compute in general. They are obtained as a limiting case of the Rényi entropy of index m, which captures the higher moments of the reduced density matrix. In this work, we study pure bipartite states associated with S3 complements of a two-component link which is a connected sum of a knot $$ \mathcal{K} $$ K and the Hopf link. For this class of links, the Chern-Simons theory provides the necessary setting to visualise the m-moment of the reduced density matrix as a three-manifold invariant Z($$ {M}_{{\mathcal{K}}_m} $$ M K m ), which is the partition function of $$ {M}_{{\mathcal{K}}_m} $$ M K m . Here $$ {M}_{{\mathcal{K}}_m} $$ M K m is a closed 3-manifold associated with the knot $$ \mathcal{K} $$ K m, where $$ \mathcal{K} $$ K m is a connected sum of m-copies of $$ \mathcal{K} $$ K (i.e., $$ \mathcal{K} $$ K #$$ \mathcal{K} $$ K . . . #$$ \mathcal{K} $$ K ) which mimics the well-known replica method. We analayse the partition functions Z($$ {M}_{{\mathcal{K}}_m} $$ M K m ) for SU(2) and SO(3) gauge groups, in the limit of the large Chern-Simons coupling k. For SU(2) group, we show that Z($$ {M}_{{\mathcal{K}}_m} $$ M K m ) can grow at most polynomially in k. On the contrary, we conjecture that Z($$ {M}_{{\mathcal{K}}_m} $$ M K m ) for SO(3) group shows an exponential growth in k, where the leading term of ln Z($$ {M}_{{\mathcal{K}}_m} $$ M K m ) is the hyperbolic volume of the knot complement S3\$$ \mathcal{K} $$ K m. We further propose that the Rényi entropies associated with SO(3) group converge to a finite value in the large k limit. We present some examples to validate our conjecture and proposal.

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“…In fact, most generally, we might expect automorphisms of the fusion rules that are not even symmetries of the modular data (e.g., as studied recently in[36]). 33 By the results of[21], these theories cannot have such fusions involving lines that carry magnetic flux 34.…”

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confidence: 94%

a×b=c in 2+1D TQFT

Buican

Radhakrishnan

2021

Quantum

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We study the implications of the anyon fusion equation a×b=c on global properties of 2+1D topological quantum field theories (TQFTs). Here a and b are anyons that fuse together to give a unique anyon, c. As is well known, when at least one of a and b is abelian, such equations describe aspects of the one-form symmetry of the theory. When a and b are non-abelian, the most obvious way such fusions arise is when a TQFT can be resolved into a product of TQFTs with trivial mutual braiding, and a and b lie in separate factors. More generally, we argue that the appearance of such fusions for non-abelian a and b can also be an indication of zero-form symmetries in a TQFT, of what we term "quasi-zero-form symmetries" (as in the case of discrete gauge theories based on the largest Mathieu group, M24), or of the existence of non-modular fusion subcategories. We study these ideas in a variety of TQFT settings from (twisted and untwisted) discrete gauge theories to Chern-Simons theories based on continuous gauge groups and related cosets. Along the way, we prove various useful theorems.

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Galois conjugation and multiboundary entanglement entropy

Cited by 9 publications

References 50 publications

Galois orbits of TQFTs: symmetries and unitarity

Galois orbits of TQFTs: symmetries and unitarity

Topological entanglement and hyperbolic volume

a×b=c in 2+1D TQFT

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