Abstract
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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Buican, M., Radhakrishnan, R. Galois conjugation and multiboundary entanglement entropy. J. High Energ. Phys. 2020, 45 (2020). https://doi.org/10.1007/JHEP12(2020)045
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DOI: https://doi.org/10.1007/JHEP12(2020)045