Interfaces and the extended Hilbert space of Chern-Simons theory

Jackson R. Fliss, Robert G. Leigh

Research output: Contribution to journalArticlepeer-review


The low energy effective field theories of (2 + 1) dimensional topological phases of matter provide powerful avenues for investigating entanglement in their ground states. In [1] 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.

Original languageEnglish (US)
Article number9
JournalJournal of High Energy Physics
Issue number7
StatePublished - Jul 1 2020


  • Chern-Simons Theories
  • Gauge Symmetry
  • Topological Field Theories
  • Topological States of Matter

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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