Related papers: Structure Constants and Integrable Bootstrap in Pl…
The recent emergence of the modern conformal bootstrap method for the study of conformal field theories (CFTs) has enabled the revisiting of old problems in classical critical phenomena described by three-dimensional CFTs. The study of such…
We present a new simple proof of the fact that certain group manifolds as well as certain homogeneous spaces G/H of dimension 4n admit a quaternionic triple of integrable complex structures that are covariantly constant with respect to the…
We present a way of constructing string solutions around non-trivial gravitational backgrounds. The proposed solutions are constructed using $N = 4$ superconformal building blocks with $\hat c = 4$. We give two different and inequivalent…
This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data…
We explore how matrix bootstrap techniques can be used to constrain matrix and tensor models at finite $N$, where $N$ is the dimension of the matrix/tensor, taking a Gaussian model with a quartic interaction as example. For matrix models,…
Hexagonal circle patterns with constant intersection angles are introduced and studied. It is shown that they are described by discrete integrable systems of Toda type. Conformally symmetric patterns are classified. Circle pattern analogs…
We reduce the computation of three point function of three spinning operators with arbitrary polarizations to a statistical mechanics problem via the hexagon formalism. The central building block of these correlation functions is the…
The D0-brane/Banks-Fischler-Shenker-Susskind matrix theory is a strongly coupled quantum system with an interesting gravity dual. We develop a scheme to derive bootstrap bounds on simple correlators in the matrix theory at infinite $N$ at…
We evaluate three-point correlation functions of single trace operators in N=4 SYM at both weak and strong coupling. We focus on the case where two of the operators belong in a SL(2) sub-sector, and are dual to string solutions in a broad…
In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; there exist stable…
Invariant theory provides more efficient tools, such as Molien generating functions and integrity bases, than basic group theory, that relies on projector techniques for the construction of symmetry--adapted polynomials in the symmetry…
We compute the fundamental correlation functions in two-dimensional rational conformal field theory, from which all other correlators can be obtained by sewing: the correlators of three bulk fields on the sphere, one bulk and one boundary…
We study scalar conformal field theories whose large $N$ spectrum is fixed by the operator dimensions of either Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a…
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…
We initiate an exploration of the conformal bootstrap for $n>4$ point correlation functions. Here we bootstrap correlation functions of the lightest scalar gauge invariant operators in planar non-abelian conformal gauge theories as their…
We calculate the leading contributions to the connected two-point functions of protected scalar operators in the defect version of N=4 SYM theory which is dual to the D5-D3 probe-brane system with k units of background gauge field flux.…
We apply the methods of modern analytic bootstrap to the critical $O(N)$ model in a $1/N$ expansion. At infinite $N$ the model possesses higher spin symmetry which is weakly broken as we turn on $1/N$. By studying consistency conditions for…
We address the novel structures arising in quantum and string integrable theories, as well as construct methods to obtain them and provide further analysis. Specifically, we implement the automorphic symmetries on periodic lattice systems…
The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large $N$ holographic theories, these fundamental observables are dual to the open string…
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…