Galois Conjugation and Multiboundary Entanglement Entropy

TL;DR

This paper explores the impact of Galois conjugation on multiboundary entanglement entropy in 3D topological quantum field theories, revealing invariance properties and connections to the topology and algebraic data of the theories.

Contribution

It establishes invariance of multiboundary entanglement entropy under Galois action for Abelian theories and extends the analysis to non-Abelian theories on specific link complements.

Findings

Proves MEE invariance under Galois action for Abelian TQFTs.

Generalizes the invariance to certain non-Abelian TQFTs.

Reveals interplay between modular data, topology, and Galois action.

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.