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The numerical conformal bootstrap has become in the last 15 years an indispensable tool for studying strongly coupled CFTs in various dimensions. Here we review the main developments in the field in the last 5 years, since the appearance of…
Applications of the bootstrap program to superconformal field theories promise unique new insights into their landscape and could even lead to the discovery of new models. Most existing results of the superconformal bootstrap were obtained…
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…
Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…
We consider conformal nets on $S^1$ of von Neumann algebras, acting on the full Fock space, arising in free probability. These models are twisted local, but non-local. We extend to the non-local case the general analysis of the modular…
We study the constraints of crossing symmetry and unitarity in general 3D Conformal Field Theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for…
We have devised an isotropic interaction potential that gives rise to negative thermal expansion (NTE) behavior in equilibrium many-particle systems in both two and three dimensions over a wide temperature and pressure range (including zero…
The crossing equations of a conformal field theory can be systematically truncated to a finite, closed system of polynomial equations. In certain cases, solutions of the truncated equations place strict bounds on the space of all unitary…
Three-dimensional theories with cubic symmetry are studied using the machinery of the numerical conformal bootstrap. Crossing symmetry and unitarity are imposed on a set of mixed correlators, and various aspects of the parameter space are…
Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero $\beta$ function as well as higher-twist effects. For example, commensurate scale relations…
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to…
In this letter we study how the exact non-perturbative integrability methods in 4D N=4 Super-Yang-Mills can work efficiently together with the numerical conformal bootstrap techniques to go beyond the spectral observables and access…
We apply the OPE inversion formula to thermal two-point functions of bosonic and fermionic CFTs in general odd dimensions. This allows us to analyze in detail the operator spectrum of these theories. We find that nontrivial thermal CFTs…
Using the gauge/gravity correspondence, we study the properties of 2-point correlation functions of finite-temperature strongly coupled gauge field theories, defined on a curved space of general spatial topology with a dual black hole…
We present a nonlinear hydrodynamical description of a conformal plasma within the framework of divergence-type theories (DTTs), which are not based on a gradient expansion. We compare the equations of the DTT and the second-order theory…
Recently an efficient numerical method has been developed to implement the constraints of crossing symmetry and unitarity on the operator dimensions and OPE coefficients of conformal field theories (CFT) in diverse space-time dimensions. It…
Non-relativistic conformal field theory describes many-body physics at unitarity. The correlation functions of the system are fixed by the requirement of conformal invariance. In this article, we discuss the correlation functions of scalar…
In this paper we study one-dimensional conformal field theory at finite temperature dual to the two-dimensional anti-de Sitter spacetime in the Rindler coordinates. We show that conformal symmetry for thermal two-point functions manifests…
We propose a numerical method to estimate one-point functions and the free-energy density of conformal field theories at finite temperature by solving the Kubo-Martin-Schwinger condition for the two-point functions of identical scalars. We…
We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential…