A note on entanglement edge modes in Chern Simons theory. (English) Zbl 1396.81046
Summary: We elaborate on the extended Hilbert space factorization of Chern Simons theory and show how this arises naturally from a proper regularization of the entangling surface in the Euclidean path integral. The regularization amounts to stretching the entangling surface into a co-dimension one surface which hosts edge modes of the Chern Simons theory when quantized on a spatial subregion. The factorized state is a regularized Ishibashi state and reproduces the well known topological entanglement entropies. We illustrate how the same factorization arises from the gluing of two spatial subregions via the entangling product defined by W. Donnelly and L. Freidel [ibid. 2016, No. 9, Paper No. 102, 45 p. (2016; Zbl 1390.83016)].
MSC:
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 58J28 | Eta-invariants, Chern-Simons invariants |
| 83E30 | String and superstring theories in gravitational theory |
| 81T45 | Topological field theories in quantum mechanics |
Keywords:
Chern-Simons theories; conformal field theory; topological field theories; topological stringsCitations:
Zbl 1390.83016References:
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