%0 Generic %1 guo2017reversal %A Guo, Meng %A Putrov, Pavel %A Wang, Juven %D 2017 %K myown %T Time Reversal, SU(N) Yang-Mills and Cobordisms: Interacting Topological Superconductors/Insulators and Quantum Spin Liquids in 3+1D %U http://arxiv.org/abs/1711.11587 %X 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.

@misc{guo2017reversal, 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 $\theta=\pi$ 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.}, added-at = {2017-12-05T03:21:17.000+0100}, author = {Guo, Meng and Putrov, Pavel and Wang, Juven}, biburl = {https://www.bibsonomy.org/bibtex/229b8e7656136bc70eda3c50f840dba85/juven}, description = {Time Reversal, SU(N) Yang-Mills and Cobordisms: Interacting Topological Superconductors/Insulators and Quantum Spin Liquids in 3+1D}, interhash = {a9a9a4af28fa2f9299e46c47ca411b2d}, intrahash = {29b8e7656136bc70eda3c50f840dba85}, keywords = {myown}, note = {cite arxiv:1711.11587Comment: 64 pages}, timestamp = {2017-12-05T03:21:17.000+0100}, title = {Time Reversal, SU(N) Yang-Mills and Cobordisms: Interacting Topological Superconductors/Insulators and Quantum Spin Liquids in 3+1D}, url = {http://arxiv.org/abs/1711.11587}, year = 2017 }