3d one-form mixed anomaly and entanglement entropy

Zhou, Yang

doi:10.1007/jhep07(2019)091

Cited by 6 publications

(4 citation statements)

References 41 publications

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“…• Anytime one considers symmetry structures, there are corresponding anomalies to contemplate. In fact, the MEE studied in this paper has been related to anomalies in [57,58]. This begs the question of how the Galois action acts on anomalies more generally.…”

Section: Discussionmentioning

confidence: 87%

Galois conjugation and multiboundary entanglement entropy

Buican

Radhakrishnan

2020

J. High Energ. Phys.

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We revisit certain natural algebraic transformations on the space of 3D topological quantum field theories (TQFTs) called “Galois conjugations.” Using a notion of multiboundary entanglement entropy (MEE) defined for TQFTs on compact 3-manifolds with disjoint boundaries, we give these abstract transformations additional physical meaning. In the process, we prove a theorem on the invariance of MEE along orbits of the Galois action in the case of arbitrary Abelian theories defined on any link complement in S3. We then give a generalization to non-Abelian TQFTs living on certain infinite classes of torus link complements. Along the way, we find an interplay between the modular data of non-Abelian TQFTs, the topology of the ambient spacetime, and the Galois action. These results are suggestive of a deeper connection between entanglement and fusion.

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Section: Discussionmentioning

confidence: 87%

Galois conjugation and multiboundary entanglement entropy

Buican

Radhakrishnan

2020

J. High Energ. Phys.

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“…For example, it would be interesting to extend the analysis of [34] to find fermionic theories with seperate holomorphic and anti-holomorphic parity symmetries, and study their anomalies. It would also be interesting to see if the reverse statement is always true, as proposed in [47,48] (See also [49]).…”

Section: Discussion and Future Directionsmentioning

confidence: 90%

Fermionization of conformal boundary states

Ebisu,

Watanabe

2021

Preprint

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We construct the complete set of boundary states of two-dimensional fermionic CFTs using that of the bosonic counterpart. We see that there are two groups of boundary conditions, which contributes to the open-string partition function by characters with integer coefficients, or with √ 2 times integer coefficients. We argue that, using the argument of [1], this √ 2 indicates a single unpaired Majorana zero mode, and that these two groups of boundary conditions are mutually incompatible.

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“…We also show that the entanglement entropies corresponding to torus links evaluated for a direct product of groups satisfy EE(G 1 × G 2 ) = EE(G 1 ) + EE(G 2 ). It is known that the entanglement entropy associated with torus link can also be used to detect one-form anomalies as shown in [21,22] for semi-simple Lie groups. It would be interesting to carry out a similar study in the context of current set-up.…”

Section: Discussionmentioning

confidence: 99%

Multi-boundary entanglement in Chern-Simons theory with finite gauge groups

Dwivedi¹,

Addazi

Zhou

et al. 2020

J. High Energ. Phys.

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We study the multi-boundary entanglement structure of the states prepared in (1+1) and (2+1) dimensional Chern-Simons theory with finite discrete gauge group G. The states in (1+1)-d are associated with Riemann surfaces of genus g with multiple S 1 boundaries and we use replica trick to compute the entanglement entropy for such states. In (2+1)-d, we focus on the states associated with torus link complements which live in the tensor product of Hilbert spaces associated with multiple T 2 . We present a quantitative analysis of the entanglement structure for both abelian and non-abelian groups. For all the states considered in this work, we find that the entanglement entropy for direct product of groups is the sum of entropy for individual groups, i.e. EE(G 1 × G 2 ) = EE(G 1 ) + EE(G 2 ). Moreover, the reduced density matrix obtained by tracing out a subset of the total Hilbert space has a positive semidefinite partial transpose on any bi-partition of the remaining Hilbert space.

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3d one-form mixed anomaly and entanglement entropy

Cited by 6 publications

References 41 publications

Galois conjugation and multiboundary entanglement entropy

Galois conjugation and multiboundary entanglement entropy

Fermionization of conformal boundary states

Multi-boundary entanglement in Chern-Simons theory with finite gauge groups

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