Per Kraus

The path integral over massless quantum fields in Minkowski space with scattering boundary conditions defines a Carrollian partition function on the null boundary. We develop this framework for non-Abelian gauge theory, both from a general perspective and through explicit examples that highlight subtle aspects of soft modes and asymptotic symmetries. These include falloff conditions, Goldstone modes and their antipodal matching, and factors of two associated with conditionally convergent integrals arising in the derivation of soft theorems. We employ path integral (rather than canonical) methods throughout.

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 bstract: The formulation of the S-matrix as a path integral with specified asymptotic boundary conditions naturally leads to the realization of a Carrollian partition function defined on the boundary of Minkowski space. This partition function, specified at past and future null infinity in the case of massless particles, generates Carrollian correlation functions that encode the S-matrix. We explore this connection, including the realization of symmetries, soft theorems arising from large gauge transformations, and the correspondence with standard momentum space amplitudes. This framework is also well-suited for embedding the Minkowski space S-matrix into the AdS/CFT duality in the large radius limit. In particular, we identify the AdS and Carrollian partition functions through a simple map between their respective asymptotic data, establishing a direct correspondence between the actions of symmetries on both sides. Our approach thus provides a coherent framework that ties together various topics extensively studied in recent and past literature.

A bstract: 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.

Pure three-dimensional gravity is a renormalizable theory with two free parameters labelled by G G and \Lambda Λ . As a consequence, correlation functions of the boundary stress tensor in AdS _3 3 are uniquely fixed in terms of one dimensionless parameter, which is the central charge of the Virasoro algebra. The same argument implies that AdS _3 3 gravity at a finite radial cutoff is a renormalizable theory, but now with one additional parameter corresponding to the cutoff location. This theory is conjecturally dual to a T\overline{T} T T ¯ -deformed CFT, assuming that such theories actually exist. To elucidate this, we study the quantum theory of boundary gravitons living on a cutoff planar boundary and the associated correlation functions of the boundary stress tensor. We compute stress tensor correlation functions to two-loop order ( G G being the loop counting parameter), extending existing tree level results. This is made feasible by the fact that the boundary graviton action simplifies greatly upon making a judicious field redefinition, turning into the Nambu-Goto action. After imposing Lorentz invariance, the correlators at this order are found to be unambiguous up to a single undetermined renormalization parameter.

The quantization of pure 3D gravity with Dirichlet boundary conditions on a finite boundary is of interest both as a model of quantum gravity in which one can compute quantities which are ``more local" than S-matrices or asymptotic boundary correlators, and for its proposed holographic duality to T\overline{T} T T ¯ -deformed CFTs. In this work we apply covariant phase space methods to deduce the Poisson bracket algebra of boundary observables. The result is a one-parameter nonlinear deformation of the usual Virasoro algebra of asymptotically AdS _3 3 gravity. This algebra should be obeyed by the stress tensor in any T\overline{T} T T ¯ -deformed holographic CFT. We next initiate quantization of this system within the general framework of coadjoint orbits, obtaining — in perturbation theory — a deformed version of the Alekseev-Shatashvili symplectic form and its associated geometric action. The resulting energy spectrum is consistent with the expected spectrum of T\overline{T} T T ¯ -deformed theories, although we only carry out the explicit comparison to \mathcal{O}(1/\sqrt{c}) ???? ( 1 / c ) in the 1/c 1 / c expansion.