Galois Conjugation and Multiboundary Entanglement Entropy

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.

arXiv comment11 figures; 3 appendices

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Cited by in corpus (6)

• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• Galois Orbits of TQFTs: Symmetries and Unitarity
• $a\times b=c$ in $2+1$D TQFT
• Semiclassical limit of topological Rényi entropy in $3d$ Chern-Simons theory
• On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures
• Topological entanglement and hyperbolic volume