Deconfined Quantum Critical Points in 3+1D

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+1D. Examples include phase transitions in quantum magnetism as well as those between Symmetry Protected Topological phases. In this work, we present several examples of Deconfined Quantum Critical Points between Symmetry Protected Topological phases in 3+1D for both bosonic and fermionic systems. These 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 will talk about 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 transitionswithin the same phase.