相关论文: Precision Bootstrap for the $\mathcal{N}=1$ Super-…

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…

We construct a conformal map from $\mathbb{R}^3$ to a three-dimensional spheriod, which includes $\mathbb{S}^3$, a double-cover of the 3-ball, and $\mathbb{R} \times \mathbb{S}^2$ as limiting cases. Using the data of the critical…

The fractal dimensions of polymer chains and high-temperature graphs in the Ising model both in three dimension are determined using the conformal bootstrap applied for the continuation of the $O(N)$ models from $N=1$ (Ising model) to $N=0$…

In this thesis, we introduce new tools for the conformal bootstrap, autoboot and qboot. Each tool solves a different step in the whole computational stack, and combined with an existing efficient tool SDPB which solves semidefinite…

We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should…

Finding a method to combine the numerical bootstrap with the analytic lightcone bootstrap is an important goal to advance the conformal bootstrap program. We propose a hybrid bootstrap method to do just that. The numerical and analytic…

This review aims to offer a pedagogical introduction to the analytic conformal bootstrap program via a journey through selected topics. We review analytic methods which include the large spin perturbation theory, Mellin space methods and…

We solve crossing equations analytically in the deep Euclidean regime. Large scaling dimension $\Delta$ tails of the weighted spectral density of primary operators of given spin in one channel are matched to the Euclidean OPE data in the…

We use modern bootstrap techniques to study half-BPS line defects in 4d N=4 superconformal theories. Specifically, we consider the 1d CFT with OSP(4*|4) superconformal symmetry living on such a defect. Our analysis is general and based only…

We develop the analytic bootstrap in several directions. First, we discuss the appearance of nonperturbative effects in the Lorentzian inversion formula, which are exponentially suppressed at large spin but important at finite spin. We show…

We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in $4d$ $\mathcal{N}=2$ superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In…

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…

Recently the OPE coefficients of the 3D Ising model universality class have been calculated by studying the two-point functions perturbed from the critical point with a relevant field. We show that this method can be applied also when the…

We describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced in previous work. To take maximal advantage of the known properties of the scalar conformal blocks for…

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…

We discuss an idea of how 3D critical exponents can be determined by Conformal Field Theory techniques.

In this thesis, we analyze unitary conformal field theories in three dimensional spaces by applying analytic conformal bootstrap techniques to correlation functions of non-scalar operators, in particular Majorana fermions. Via the analysis…

We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising…

The dimensional reductions in the branched polymer and the random field Ising model (RFIM) are discussed by a conformal bootstrap method. The small size minors are applied for the evaluations of the scale dimensions of these two models and…

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…