  Deconfined quantum critical points are characterized by the presence of an
emergent gauge field and exotic fractionalized particles, which exist as
well-defined excitations only at the critical point. We here demonstrate the
existence of quantum critical points described by an emergent tensor gauge
theory featuring subdimensional excitations, in close relation to fracton
theories. We begin by reexamining a previously studied deconfined quantum
critical point between two valence bond solid (VBS) phases on a bilayer
honeycomb lattice. We show that the critical theory maps onto a rank-two tensor
gauge theory featuring one-dimensional particles. In a slightly different
context, the same tensor gauge theory also describes a deconfined quantum
critical point between a two-dimensional superfluid and a finite-momentum Bose
condensate, both of which are dual to rank-one gauge theories. This represents
an entirely new class of deconfined quantum criticality, in which a critical
tensor gauge theory arises on top of a stable conventional gauge theory.
Furthermore, we propose that this quantum critical point gives rise to a new
finite-temperature phase of bosons, behaving as an exciton Bose condensate, in
which excitons (boson-hole pairs) are condensed but individual bosons are not.
We discuss how small modifications of this theory give rise to the stable
quantum "exciton Bose liquid" phase studied by Paramekanti, Balents, and
Fisher.
