A bstract The main objective of this work is to isolate Effective Field Theory scattering
amplitudes in the space of non-perturbative two-to-two amplitudes, using the S-matrix …

A bstract We study families of one-dimensional CFTs relevant for describing gapped QFTs in
AdS 2. Using the Polyakov bootstrap as our main tool, we explain how S-matrices emerge …

We consider scalar QED with Nf flavors in AdSD. For D< 4 the theory is strongly-coupled in
the IR. We use the spin 1 spectral representation to compute and efficiently resum the …

A bstract In this work, we initiate a positive semi-definite numerical bootstrap program for
multi-point correlators. Considering six-point functions of operators on a line, we reformulate …

We derive a dispersion relation for two-point correlation functions in defect conformal field
theories. The correlator is expressed as an integral over a (single) discontinuity that is …

A bstract For QFTs in AdS the boundary correlation functions remain conformal even if the
bulk theory has a scale. This allows one to constrain RG flows with numerical conformal …

We introduce manifestly crossing-symmetric expansions for arbitrary systems of 1D CFT
correlators. These expansions are given in terms of certain Polyakov blocks which we define …

We introduce manifestly crossing-symmetric expansions for arbitrary systems of 1D CFT
correlators. These expansions are given in terms of certain Polyakov blocks which we define …

We use commutativity of null-integrated operators on the same null plane to construct
dispersive CFT sum rules for spinning operators. The contribution of heavy blocks to these …

In this thesis, we consider two approaches to the study of correlation functions in
onedimensional defect Conformal Field Theories (dCFT 1), in particular those defined by 1/2 …