Related papers: Conformal Bootstrap in Mellin Space

We consider Deep Inelastic Scattering (DIS) thought experiments in unitary Conformal Field Theories (CFTs). We explore the implications of the standard dispersion relations for the OPE data. We derive positivity constraints on the OPE…

We introduce a non-unitary-compatible numerical bootstrap strategy based on the statistical stability of OPE data inferred from crossing at multiple cross-ratios. For a trial spectrum, crossing determines OPE coefficients whose residual…

We introduce a novel method to bootstrap crossing equations in Conformal Field Theory and apply it to finite temperature theories on $S^1\times \mathbb{R}^{d-1}$. The proposed approach does not rely on positivity constraints and does not…

We take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| << |v| < 1. We prove that every CFT with a scalar operator…

Higher-point correlation functions encode the data of infinitely many 4-point correlators in conformal field theory (CFT). In this paper, we develop new tools to efficiently extract this data from multi-point crossing equations. Concretely,…

This is a set of introductory lecture notes on conformal field theory. Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. It begins with a…

Conformal field theory (CFT) is the key to various critical phenomena. So far, most of studies focus on the critical exponents of various universalities, corresponding to conformal dimensions of CFT primary fields. However, other important…

We consider a conformal field theory in the presence of a boundary, and explain how two-point correlators of mixed bulk-local operators can be bootstrapped by exploiting the analytical structure of the conformal blocks. This yields the…

We use large spin perturbation theory and the Lorentzian inversion formula to compute order-$\varepsilon$ corrections to mixed correlators in the $O(n)$ Wilson-Fisher CFT in $4 - \varepsilon$ dimensions. In particular, we find the scaling…

We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion…

In this work we initiate the conformal bootstrap program for ${\mathcal N}=2$ superconformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and…

Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…

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 study the conformal bootstrap of 1D CFTs on the straight Maldacena-Wilson line in 4D ${\cal N}=4$ super-Yang-Mills theory. We introduce an improved truncation scheme with an 'OPE tail' approximation and use it to reproduce the…

The fundamental ingredients that build the observables in conformal field theory are the spectrum of operators and the OPE coefficients, or equivalently, the two- and three-point functions of the theory. Recently an inversion formula…

We clarify the relationships between different approaches to the conformal bootstrap. A central role is played by the so-called extremal functionals. They are linear functionals acting on the crossing equation which are directly responsible…

We review the algebraic and analytic aspects of the conformal field theory (CFT) and its relation to the stochastic Loewner evolution (SLE) in an example of the Ising model. We obtain the scaling limit of the correlation functions of Ising…

We prove convergence and compatibility of iterated bulk and boundary operator product expansions (OPEs) in two-dimensional conformal field theory with locally $C_1$-cofinite chiral symmetry. For each tree, we give an explicit domain of…

The 3D Bondi-Metzner-Sachs (BMS$_3$) algebra that is the asymptotic symmetry algebra at null infinity of the $1+2$D asymptotically flat space-time is isomorphic to the $1+1$D Carrollian conformal algebra. Building on this connection,…

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…