Tunneling Topological Vacua via Extended Operators: TQFT Spectra and Boundary Deconfinement in Various Dimensions

Juven Wang Institute for Advanced Study, Princeton Kantaro Ohmori Institute for Advanced Study, Princeton Pavel Putrov Institute for Advanced Study, Princeton Yunqin Zheng Princeton University Hai Lin Yau Mathematical Sciences Center, Tsinghua University Peng Gao Harvard University Shing-Tung Yau Harvard University

Mathematical Physics mathscidoc:1802.22001

Distinct quantum vacua of topologically ordered states can be tunneled into each other, not by local operators, but via extended operators. The possible applications include condensed matter and quantum cosmology. We present a straightforward approach to calculate the partition function on various manifolds and ground state degeneracy (GSD), mainly based on continuum/cochain Topological Quantum Field Theories (TQFT), in any dimension. This information can be related to the counting of extended operators of bosonic/fermionic TQFT. On the lattice scale, anyonic particles/strings live at the ends of line/surface operators. Certain systems in different dimensions are related to each other through dimensional reduction schemes, analogous to decategorification. We consider situations where a TQFT lives on (1) a closed spacetime or (2) a spacetime with boundary, such that both the bulk and boundary are fully-gapped and long-range entangled (LRE). Anyonic excitations can be deconfined on the boundary. We introduce new exotic topological interfaces on which neither particle nor string excitations alone condensed, but only fuzzy-composite objects of extended operators can end (e.g. a string-like fuzzy-composite object formed by a set of particles can end on a special 2+1D boundary of 3+1D bulk). We explore the relations between group extension constructions and partially breaking constructions (e.g. 0-form/higher-form/“composite” breaking) of topological boundaries, after gauging. We comment on the implications of entanglement entropy for some of such LRE systems.
High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Strongly Correlated Electrons (cond-mat.str-el); Algebraic Topology (math.AT); Topological Phases of Matter; Gauge theories; TQFT; Quantum Field Theories
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  • https://arxiv.org/abs/1801.05416, with 52 pages
@inproceedings{juventunneling,
  title={Tunneling Topological Vacua via Extended Operators: TQFT Spectra and Boundary Deconfinement in Various Dimensions},
  author={Juven Wang, Kantaro Ohmori, Pavel Putrov, Yunqin Zheng, Hai Lin, Peng Gao, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180208114931029172915},
}
Juven Wang, Kantaro Ohmori, Pavel Putrov, Yunqin Zheng, Hai Lin, Peng Gao, and Shing-Tung Yau. Tunneling Topological Vacua via Extended Operators: TQFT Spectra and Boundary Deconfinement in Various Dimensions. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180208114931029172915.
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