Title: Deconfined quantum critical points: symmetries and dualities,
Abstract: The deconfined quantum critical point (QCP), separating the Néel and
valence bond solid phases in a 2D antiferromagnet, was proposed as an example
of $2+1$D criticality fundamentally different from standard
Landau-Ginzburg-Wilson-Fisher {criticality}. In this work we present multiple
equivalent descriptions of deconfined QCPs, and use these to address the
possibility of enlarged emergent symmetries in the low energy limit. The
easy-plane deconfined QCP, besides its previously discussed self-duality, is
dual to $N_f = 2$ fermionic quantum electrodynamics (QED), which has its own
self-duality and hence may have an O(4)$\times Z_2^T$ symmetry. We propose
several dualities for the deconfined QCP with ${\mathrm{SU}(2)}$ spin symmetry
which together make natural the emergence of a previously suggested $SO(5)$
symmetry rotating the Néel and VBS orders. These emergent symmetries are
implemented anomalously. The associated infra-red theories can also be viewed
as surface descriptions of 3+1D topological paramagnets, giving further insight
into the dualities. We describe a number of numerical tests of these dualities.
We also discuss the possibility of "pseudocritical" behavior for deconfined
critical points, and the meaning of the dualities and emergent symmetries in
such a scenario.