  A long-standing problem in the study of topological phases of matter has been
to understand the types of fractional topological insulator (FTI) phases
possible in 3+1 dimensions. Unlike ordinary topological insulators of free
fermions, FTI phases are characterized by fractional $\Theta$-angles,
long-range entanglement, and fractionalization. Starting from a simple family
of $\mathbb{Z}_N$ lattice gauge theories due to Cardy and Rabinovici, we
develop a class of FTI phases based on the physical mechanism of oblique
confinement and the modern language of generalized global symmetries. We dub
these phases oblique topological insulators. Oblique TIs arise when dyons --
bound states of electric charges and monopoles -- condense, leading to FTI
phases characterized by topological order, emergent one-form symmetries, and
gapped boundary states not realizable in 2+1-D alone. Based on the lattice
gauge theory, we present continuum topological quantum field theories (TQFTs)
for oblique TI phases involving fluctuating one-form and two-form gauge fields.
We show explicitly that these TQFTs capture both the generalized global
symmetries and topological orders seen in the lattice gauge theory. We also
demonstrate that these theories exhibit a universal "generalized
magnetoelectric effect" in the presence of two-form background gauge fields.
Moreover, we characterize the possible boundary topological orders of oblique
TIs, finding a new set of boundary states not studied previously for these
kinds of TQFTs.
