Abstract
We introduce a web of strongly correlated interacting 3+1D topological
superconductors/insulators of 10 particular global symmetry groups of Cartan
classes, realizable in electronic condensed matter systems, and their
generalizations. The symmetries include SU(N), SU(2), U(1), fermion parity,
time reversal and relate to each other through symmetry embeddings. We overview
the lattice Hamiltonian formalism. We complete the list of bulk
symmetry-protected topological invariants (SPT invariants/partition funnctions
that exhibit boundary 't Hooft anomalies) via cobordism calculations, matching
their full classification. We also present explicit 4-manifolds that detect
these SPTs. On the other hand, once we dynamically gauge part of their global
symmetries, we arrive at various new phases of SU(N) Yang-Mills (YM),
realizable as quantum spin liquids with emergent gauge fields. We discuss how
coupling YM theories to time reversal-SPTs affects the strongly coupled
theories at low energy. For example, we point out a possibility of having two
deconfined gapless time-reversal symmetric SU(2) YM theories at $þeta=\pi$ as
two distinct conformal field theories, which although are indistinguishable by
gapped SPT states nor by correlators of local operators on oriented spacetimes,
can be distinguished on non-orientable spacetimes or potentially by correlators
of extended operators.
Description
Time Reversal, SU(N) Yang-Mills and Cobordisms: Interacting Topological
Superconductors/Insulators and Quantum Spin Liquids in 3+1D
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