Related papers: The momentum-space conformal bootstrap in 2d
In this paper, we Fourier transform the Wightman function concerning energy and angular momentum on the $S^{D-1}$ spatial slice in radial quantization in $D=2,3$ dimensions. In each case, we use the conformal Ward Identities to solve…
General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the…
We present a Feynman integral representation for the general momentum-space scalar $n$-point function in any conformal field theory. This representation solves the conformal Ward identities and features an arbitrary function of $n(n-3)/2$…
We construct a crossing symmetric basis for conformal four-point functions in momentum space by requiring consistent factorization. Just as scattering amplitudes factorize when the intermediate particle is on-shell, non-analytic parts of…
This paper explores the numerical conformal bootstrap in general spacetime dimensions through the lens of a distinct category of analytic functionals, previously employed in two-dimensional studies. We extend the application of these…
We study analytically the constraints of the conformal bootstrap on the low-lying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals…
In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic…
In this thesis we study the momentum space approach to the solution of the CWI's of CFT's in higher dimensions. Our work's goal is to illustrate the essential steps needed to build tensor correlators starting from the scalar solutions, for…
Analyticity and crossing properties of four point function are investigated in conformal field theories in the frameworks of Wightman axioms. A Hermitian scalar conformal field, satisfying the Wightman axioms, is considered. The crucial…
Conformal field theories that exhibit spontaneous breaking of conformal symmetry (a moduli space of vacua) must satisfy a set of bootstrap constraints, involving the usual data (scaling dimensions and OPE coefficients) as well as new data…
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
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…
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…
We develop a novel numerical bootstrap for unitary, crossing-symmetric conformal field theories, focusing on moment observables defined as weighted averages over conformal data. Providing a global and coarse-grained probe of the operator…
We find the general solution of the conformal Ward identities for scalar $n$-point functions in momentum space and in general dimension. The solution is given in terms of integrals over $(n-1)$-simplices in momentum space. The $n$ operators…
In physics, it is believed that the consistency of two dimensional conformal field theory follows from the bootstrap equation. In this paper, we introduce the notion of a full vertex algebra by analyzing the bootstrap equation, which is a…
It is shown how to obtain conformal blocks from embedding space with the help of the operator product expansion. The minimal conformal block originates from scalar exchange in a four-point correlation functions of four scalars. All…
Our previous work [1] constructed, in three-dimensional momentum space, a manifestly crossing symmetric basis for scalar conformal four-point functions, based on the factorization property proposed by Polyakov. This work extends this…
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…