  Continuous quantum phase transitions that are beyond the conventional
paradigm of fluctuations of a symmetry breaking order parameter are challenging
for theory. These phase transitions often involve emergent deconfined gauge
fields at the critical points as demonstrated in 2+1-dimensions. Examples
include phase transitions in quantum magnetism as well as those between
Symmetry Protected Topological phases. In this paper, we present several
examples of Deconfined Quantum Critical Points (DQCP) between Symmetry
Protected Topological phases in 3+1-D for both bosonic and fermionic systems.
Some of the critical theories can be formulated as non-abelian gauge theories
either in their Infra-Red free regime, or in the conformal window when they
flow to the Banks-Zaks fixed points. We explicitly demonstrate several
interesting quantum critical phenomena. We describe situations in which the
same phase transition allows for multiple universality classes controlled by
distinct fixed points. We exhibit the possibility - which we dub "unnecessary
quantum critical points" - of stable generic continuous phase transitions
within the same phase. We present examples of interaction driven band-theory-
forbidden continuous phase transitions between two distinct band insulators.
The understanding we develop leads us to suggest an interesting possible 3+1-D
field theory duality between SU(2) gauge theory coupled to one massless adjoint
Dirac fermion and the theory of a single massless Dirac fermion augmented by a
decoupled topological field theory.
