Seminars

Title: Landau diagrams in AdS and S-matrices from conformal correlators

Abstract: Quantum field theories in AdS generate conformalcorrelation functions on the boundary, and in the limit where AdS is nearly flat one should be able to extract an S-matrix from such correlators. We discuss a particularly simple position-space procedure to do so. It features a direct map from boundary positionsto (on-shell) momenta and thereby relates cross ratios to Mandelstam invariants. This recipe succeeds in several examples, includes the momentum-conserving delta functions, and can be shown to imply the two proposals based on Mellin space and on the OPE data.Interestingly the procedure does not always work: the Landau singularities of a Feynman diagram are shown to be part of larger regions, to be called `bad regions’, where the flat-space limit of the Witten diagram diverges. To capture these divergences we introducethe notion of Landau diagrams in AdS. As in flat space, these describe on-shell particles propagating over large distances in a complexified space, with a form of momentum conservation holding at each bulk vertex. As an application we recover the anomalousthreshold of the four-point triangle diagram at the boundary of a bad region.

Title: Boundary conditions for a free scalar field

Abstract:

In the first part of the talk, I will consider the problem of classifying the conformal boundary conditions (b.c.) for the free scalar CFT. We will see how to tackle this problem using conformal bootstrap techniques. In the case of 4d bulk, I will show ournumerical results, which feature a “kink” that indicates the existence of a non-trivial “interacting” b.c., besides the obvious Neumann and Dirichlet “free” b.c.’s.

In the second part of the talk, I will discuss the RG flow of a 4d free scalar field coupled to large N vector models on the boundary. The (classically marginal) coupling involves the boundary mode of the scalar and the O(N) single-trace scalar operator. Iwill explain that the resulting RG connects two fixed points with bulk and boundary decoupled, and the local 3d sector is the free vector model in one end, and the critical one in the other end. This same RG admits two weak-strong dual descriptions, one fromthe free end, and one from the critical end.