Related papers: Snowmass White Paper: The Analytic Conformal Boots…
In this thesis we study classical aspects of superconformal field theory via symmetry principles. Specifically, by employing the powerful setup of conformal superspace, we obtain a plethora of new results in the fields of geometric and…
The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal…
The Schwinger-Dyson equations for Green functions and 3-vertexes in planar approximation used 50 years ago in the earlier theory of conformal bootstrap are written in frames of the AdS/CFT correspondence. The technique of "Wightman-Witten"…
We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal…
We formulate the conformal bootstrap approach to four--fermion theory at its strong coupling fixed point in dimensions $2<d<4$. We present a solution of the bootstrap equations in the five--vertex approximation. We show that the bootstrap…
We study a general class of functionals providing an analytic handle on the conformal bootstrap equations in one dimension. We explicitly identify the extremal functionals, corresponding to theories saturating conformal bootstrap bounds, in…
Conformal field theories have been extremely useful in our quest to understand physical phenomena in many different branches of physics, starting from condensed matter all the way up to high energy. Here we discuss applications of…
We demonstrate how table-top settings combining hyperbolic lattices with nonlinear dynamics universally encode aspects of the bulk-boundary-correspondence between gravity in anti-de-Sitter (AdS) space and conformal field theory (CFT). Our…
These lectures were given at the Weizmann Institute in the spring of 2019. They are intended to familiarize students with the nuts and bolts of the numerical bootstrap as efficiently as possible. After a brief review of the basics of…
The integrable bootstrap program allows one to express the tempered distributions associated with the multipoint functions of the integrable 1+1 dimensional Sinh-Gordon quantum field theory by means of explicit series. The convergence of…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
Boundary conformal field theory (BCFT) is simply the study of conformal field theory (CFT) in domains with a boundary. It gains its significance because, in some ways, it is mathematically simpler: the algebraic and geometric structures of…
A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy…
We present a new computational framework combining coarse-graining techniques with bootstrap methods to study quantum many-body systems. The method efficiently computes rigorous upper and lower bounds on both zero- and finite-temperature…
In this review we study quantum field theories and conformal field theories with global symmetries in the limit of large charge for some of the generators of the symmetry group. At low energy the sectors of the theory with large charge are…
We use the numerical conformal bootstrap to study boundary quantum electrodynamics, the theory of a four dimensional photon in a half space coupled to charged conformal matter on the boundary. This system is believed to be a boundary…
We apply analytic conformal bootstrap ideas in Mellin space to conformal field theories with $O(N)$ symmetry and cubic anisotropy. We write down the conditions arising from the consistency between the operator product expansion and crossing…
We present a unified framework for the study of late time cosmic acceleration. Using methods of effective field theory, we show that existing proposals for late time acceleration can be subsumed in a single framework, rather than many…
The conformal method developed in the 1970s and the more recent Lagrangian and Hamiltonian conformal thin-sandwich methods are techniques for finding solutions of the Einstein constraint equations. We show that they are manifestations of a…
We use analytic bootstrap techniques for a CFT with an interface or a boundary. Exploiting the analytic structure of the bulk and boundary conformal blocks we extract the CFT data. We further constrain the CFT data by applying the equation…