In recent years soft factorization theorems in scattering amplitudes have been reinterpreted as conservation laws of asymptotic charges. In gauge, gravity, and higher spin theories the asymptotic charges can be understood as canonical generators of large gauge symmetries. Such a symmetry interpretation has been so far missing for scalar soft theorems. We remedy this situation by treating the massless scalar field in terms of a dual two-form gauge field. We show that the asymptotic charges associated to the scalar soft theorem can be understood as generators of large gauge transformations of the dual two-form field.The dual picture introduces two new puzzles: the charges have very unexpected Poisson brackets with the fields, and the monopole term does not always have a dual gauge transformation interpretation. We find analogs of these two properties in the Kramers-Wannier duality on a finite lattice, indicating that the free scalar theory has new edge modes at infinity that canonically commute with all the bulk degrees of freedom.

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In this work we construct holographic boundary theories for linearized 3D gravity, for a general family of finite or quasi-local boundaries. These boundary theories are directly derived from the dynamics of 3D gravity by computing the effective action for a geometric boundary observable, which measures the geodesic length from a given boundary point to some centre in the bulk manifold. We identify the general form for these boundary theories and find that these are Liouville like with a coupling to the boundary Ricci scalar. This is illustrated with various examples, which each offer interesting insights into the structure of holographic boundary theories. Contents* Electronic address: sasanteATperimeterinstitute.ca † Electronic address: bdittrichATperimeterinstitute.ca ‡ Electronic address: fhopfmuellerATperimeterinstitute.ca VI. Twisted thermal AdS space with finite boundary 23 A. Equations of motion and evaluation of the action 23 B. One loop correction from the dual field 25 VII. Flat space with spherical boundary 25 A. Solutions to the equations of motion 26 B. Evaluation of the action 27 VIII. Discussion and outlook 29 A. Conventions and Gauss-Codazzi relations 31 B. Vector basis for induced perturbations 31 C. Second order of the Hamilton-Jacobi functional 34 D. Evaluation of the commutator [∂ ⊥ , ∆] 36 E. Solutions of the equations of motion for the case 2 R = 0 37 F. Equations of motion in spherical coordinates 40 G. Lagrange multiplier dependent boundary terms 42 H. Geodesic length to first order in metric perturbations 43 I. Smoothness conditions for the metric at r = 0 44 J. On effective actions 45 K. Spherical tensor harmonics 46 References 46 9The boundary fluctuations for which one can and cannot find solutions for lapse and shift can be read off from (5.13). Eg. allowing only for non-vanishing fluctuations γ θθ still allows for a solution.

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