Quantum phase transitions beyond the Landau-Ginzburg paradigm and   supersymmetry
  We make connections between studies in the condensed matter literature on quantum phase transitions in square lattice antiferromagnets, and results in the particle theory literature on abelian supersymmetric gauge theories in 2+1 dimensions. In particular, we point out that supersymmetric U(1) gauge theories (with particle content similar, but not identical, to those of theories of doped antiferromagnets) provide rigorous examples of quantum phase transitions which do not obey the Landau-Ginzburg-Wilson paradigm (often referred to as transitions realizing "deconfined criticality"). We also make connections between supersymmetric mirror symmetries and condensed matter particle-vortex dualities. 
Subir Sachdev and Xi Yin