Diffeomorphism symmetry, triangulation independence and constraints in discrete gravity

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Diffeomorphism symmetry is the underlying symmetry of general
relativity and deeply intertwined with its dynamics. The notion of
diffeomorphism symmetry is however obscured in discrete gravity, which
underlies most of the current quantum gravity models. We will propose
a notion of diffeomorphism symmetry in discrete models and find that
such a symmetry is weakly broken in many models. This is connected to
the problem of finding a consistent canonical dynamics for discrete
gravity. Finally we will discuss methods to construct models with
exact symmetries and elaborate on the connection between
diffeomorphism symmetry and triangulation independence.