We explore a formulation of the Smatrix in terms of the path integral with specified asymptotic data, as originally proposed by Arefeva, Faddeev, and Slavnov. In the tree approximation the Smatrix is equal to the exponential of the classical action evaluated onshell. This formulation is wellsuited to questions involving asymptotic symmetries, as it avoids reference to nongauge/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 Smatrix in curved spacetime, including particle production due to a time dependent metric.
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A<sc>bstract</sc> Free, publiclyaccessible full text available October 1, 2024 
A bstract Pure gravity in AdS 3 is a theory of boundary excitations, most simply expressed as a constrained free scalar with an improved stress tensor that is needed to match the BrownHenneaux central charge. Excising a finite part of AdS gives rise to a static gauge NambuGoto action for the boundary graviton. We show that this is the $$ T\overline{T} $$ T T ¯ deformation of the infinite volume theory, as the effect of the improvement term on the deformed action can be absorbed into a field redefinition. The classical gravitational stress tensor is reproduced order by order by the $$ T\overline{T} $$ T T ¯ trace equation. We calculate the finite volume energy spectrum in static gauge and find that the trace equation imposes sufficient constraints on the ordering ambiguities to guarantee agreement with the lightcone gauge prediction. The correlation functions, however, are not completely fixed by the trace equation. We show how both the gravitational action and the $$ T\overline{T} $$ T T ¯ deformation allow for finite improvement terms, and we match these to the undetermined total derivative terms in Zamolodchikov’s point splitting definition of the $$ T\overline{T} $$ T T ¯ operator.more » « less

Pure threedimensional gravity is a renormalizable theory with twofree parameters labelled by
andG $G$ .As a consequence, correlation functions of the boundary stress tensor inAdS\Lambda $\Lambda $ are uniquely fixed in terms of one dimensionless parameter, which is thecentral charge of the Virasoro algebra. The same argument implies thatAdS_3 ${}_{3}$ gravity at a finite radial cutoff is a renormalizable theory, but nowwith one additional parameter corresponding to the cutoff location. Thistheory is conjecturally dual to a_3 ${}_{3}$ deformedCFT, assuming that such theories actually exist. To elucidate this, westudy the quantum theory of boundary gravitons living on a cutoff planarboundary and the associated correlation functions of the boundary stresstensor. We compute stress tensor correlation functions to twoloop order(T\overline{T} $T\overline{T}$ being the loop counting parameter), extending existing tree levelresults. This is made feasible by the fact that the boundary gravitonaction simplifies greatly upon making a judicious field redefinition,turning into the NambuGoto action. After imposing Lorentz invariance,the correlators at this order are found to be unambiguous up to a singleundetermined renormalization parameter.G $G$ 
The quantization of pure 3D gravity with Dirichlet boundaryconditions on a finite boundary is of interest both as a model ofquantum gravity in which one can compute quantities which are ``morelocal" than Smatrices or asymptotic boundary correlators, and forits proposed holographic duality to T\overline{T} T T ¯ deformedCFTs. In this work we apply covariant phase space methods to deduce thePoisson bracket algebra of boundary observables. The result is aoneparameter nonlinear deformation of the usual Virasoro algebra ofasymptotically AdS _3 3 gravity. This algebra should be obeyed by the stress tensor in any T\overline{T} T T ¯ deformedholographic CFT. We next initiate quantization of this system within thegeneral framework of coadjoint orbits, obtaining — in perturbationtheory — a deformed version of the AlekseevShatashvili symplectic formand its associated geometric action. The resulting energy spectrum isconsistent with the expected spectrum of T\overline{T} T T ¯ deformedtheories, although we only carry out the explicit comparison to \mathcal{O}(1/\sqrt{c}) 𝒪 ( 1 / c ) in the 1/c 1 / c expansion.more » « less