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A<sc>bstract</sc> We study various aspects of codimension one defects in free scalar field theory, with particular emphasis on line defects in two-dimensions. These defects are generically non-conformal, but include conformal and topological defects as special cases. Our analysis is based on the interplay between two complementary descriptions, the first involving matching conditions imposed on fields and their derivatives across the defect, and the second on the resummation of perturbation theory in terms of renormalized defect couplings. Using either description as appropriate we compute a variety of observables: correlators of fields in the presence of such defects; the defect anomalous dimension; multiple defects and their fusion; canonical quantization and instabilities; ring shaped defects with application to the g-theorem and the entanglement entropy of accelerating defects; defects on the torus and Cardy formulas for the asymptotic density of states of the defect Hilbert space; and quenches produced by spacelike defects. The simplicity of the model allows for explicit computation of all these quantities, and provides a starting point for more complicated theories involving interactions. 

A<sc>bstract</sc> We explore a formulation of the S-matrix in terms of the path integral with specified asymptotic data, as originally proposed by Arefeva, Faddeev, and Slavnov. In the tree approximation the S-matrix is equal to the exponential of the classical action evaluated on-shell. This formulation is well-suited to questions involving asymptotic symmetries, as it avoids reference to non-gauge/diffeomorphism invariant bulk correlators or sources at intermediate stages. We show that the soft photon theorem, originally derived by Weinberg and more recently connected to asymptotic symmetries by Strominger and collaborators, follows rather simply from invariance of the action under large gauge transformations applied to the asymptotic data. We also show that this formalism allows for efficient computation of the S-matrix in curved spacetime, including particle production due to a time dependent metric. 

A bstract We undertake a general study of the boundary (or edge) modes that arise in gauge and gravitational theories defined on a space with boundary, either asymptotic or at finite distance, focusing on efficient techniques for computing the corresponding boundary action. Such actions capture all the dynamics of the system that are implied by its asymptotic symmetry group, such as correlation functions of the corresponding conserved currents. Working in the covariant phase space formalism, we develop a collection of approaches for isolating the boundary modes and their dynamics, and illustrate with various examples, notably AdS 3 gravity (with and without a gravitational Chern-Simons terms) subject to assorted boundary conditions.