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arXiv · 1912.04937

Galois Conjugation and Multiboundary Entanglement Entropy

Matthew Buican·Rajath Radhakrishnan
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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 $S^3$. 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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Matthew Buican, Rajath Radhakrishnan. 2019-12-10. Galois Conjugation and Multiboundary Entanglement Entropy. https://doi.org/10.1007/jhep12(2020)045

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