  Rydberg atoms in optical tweezer arrays provide a playground for
nonequilibrium quantum many-body physics. The PXP model describes the dynamics
of such systems in the strongly interacting Rydberg blockade regime and notably
exhibits weakly nonergodic dynamics due to quantum many-body scars. Here, we
study the PXP model in a strong staggered external field, which has been
proposed to manifest quasiparticle confinement in light of a mapping to a
lattice gauge theory. We characterize this confining regime using both
numerical exact diagonalization and perturbation theory around the strong-field
limit. In addition to the expected emergent symmetry generated by the staggered
field, we find a second emergent symmetry that is special to the PXP model. The
interplay between these emergent symmetries and the Rydberg blockade constraint
dramatically slows down the system's dynamics beyond naive expectations. We
devise a nested Schrieffer-Wolff perturbation theory to properly account for
the new emergent symmetry and show that this treatment is essential to
understand the numerically observed relaxation time scales. We also discuss
connections to Hilbert space fragmentation and trace the origin of the new
emergent symmetry to a "nearly-$SU(2)$" algebra discovered in the context of
many-body scarring.
