Is deconfined quantum criticality in frustrated antiferromagnets ruled out by generic fluctuation induced first order behavior?

Recently, it was argued that quantum phase transitions in frustrated two dimensional antiferromagnets can be radically different from their classical counterparts with as a highlight, the "deconfined critical points" exhibiting fractionalization of quantum numbers due to Berry phase effects. However, field theoretical descriptions rest on a naive coarse graining of the microscopic lattice model assuming order parameter fluctuations on small scales to be smooth. We have developed a novel renormalization approach for such systems which incorporates fluctuations on small scales in a natural way, and is fully respecting the underlying lattice structure and the frustration mechanism. According to our findings, another profound phenomenon is around the corner: a fluctuation induced first order transition.