  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 new SU(N)
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 field theories of
bulk symmetry-protected topological invariants (SPT invariants/partition
functions 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 in various new phases of SU(N) Yang-Mills (YM)
gauge theories, analogous to 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
secretly indistinguishable by correlators of local operators on orientable
spacetimes nor by gapped SPT states, can be distinguished on non-orientable
spacetimes or potentially by correlators of extended operators.
