Holonomies and Boundary Symmetries in the Discrete BF Formulation of Carroll Dilaton Gravity

Abstract: We construct a discrete realization of two-dimensional Carroll dilaton gravity based on a BF-type gauge structure with holonomy variables on lattice links. The bulk theory remains topological, while the physical dynamics is encoded in boundary degrees of freedom. Imposing admissible boundary conditions, we derive the asymptotic symmetry structure directly at the lattice level. The least restrictive conditions yield an affine extension of the Carroll algebra, while additional constraints reduce the symmetry to a conformal sector governed by a discrete Virasoro-type algebra. In the continuum limit, the lattice symmetry structure reproduces the expected affine Carroll algebra together with its conformal reduction. The construction therefore provides the ultra-relativistic counterpart of discrete Jackiw-Teitelboim(JT) gravity.