Interfaces and the extended Hilbert space of Chern-Simons theory
arXiv:2004.05123 · doi:10.1007/JHEP07(2020)009
Abstract
The low energy effective field theories of dimensional topological phases of matter provide powerful avenues for investigating entanglement in their ground states. In \cite{Fliss:2017wop} the entanglement between distinct Abelian topological phases was investigated through Abelian Chern-Simons theories equipped with a set of topological boundary conditions (TBCs). In the present paper we extend the notion of a TBC to non-Abelian Chern-Simons theories, providing an effective description for a class of gapped interfaces across non-Abelian topological phases. These boundary conditions furnish a defining relation for the extended Hilbert space of the quantum theory and allow the calculation of entanglement directly in the gauge theory. Because we allow for trivial interfaces, this includes a generic construction of the extended Hilbert space in any (compact) Chern-Simons theory quantized on a Riemann surface. Additionally, this provides a constructive and principled definition for the Hilbert space of effective ground states of gapped phases of matter glued along gapped interfaces. Lastly, we describe a generalized notion of surgery, adding a powerful tool from topological field theory to the gapped interface toolbox.
arXiv comment46 pages, many figures, 1 appendix; v2: fixed affiliations, minor revisions, added references
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