Related papers: An Algebraic Approach to the Analytic Bootstrap

A new (algebraic) approximation scheme to find {\sl global} solutions of two point boundary value problems of ordinary differential equations (ODE's) is presented. The method is applicable for both linear and nonlinear (coupled) ODE's whose…

We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs), both generic and holographic. We point out that in large $N$ CFTs with a large gap to single-trace higher spin operators, the…

We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave…

Over the last several decades, improvements in the fields of analytic combinatorics and computer algebra have made determining the asymptotic behaviour of sequences satisfying linear recurrence relations with polynomial coefficients largely…

In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus…

We use the conformal bootstrap to study conformal field theories with $O(N)$ global symmetry in $d=5$ and $d=5.95$ spacetime dimensions that have a scalar operator $\phi_i$ transforming as an $O(N)$ vector. The crossing symmetry of the…

We initiate the analytical functional bootstrap study of conformal field theories with large $N$ limits. In this first paper we particularly focus on the 1D $O(N)$ vector bootstrap. We obtain a remarkably simple bootstrap equation from the…

We employ chordal decomposition to reformulate a large and sparse semidefinite program (SDP), either in primal or dual standard form, into an equivalent SDP with smaller positive semidefinite (PSD) constraints. In contrast to previous…

In this work, we introduce a method based on piecewise polynomial interpolation to enclose rigorously solutions of nonlinear ODEs. Using a technique which we call a priori bootstrap, we transform the problem of solving the ODE into one of…

We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster…

We develop an approach to construct local bulk operators in a CFT to order $1/N^2$. Since 4-point functions are not fixed by conformal invariance we use the OPE to categorize possible forms for a bulk operator. Using previous results on…

We generalize the computation of anomalous dimension and correction to OPE coefficients at finite conformal spin considered recently in \cite{arXiv:1806.10919, arXiv:1808.00612} to arbitrary space-time dimensions. By using the inversion…

We consider conformal field theories with slightly broken higher spin symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in the double light-cone limit and solve for the anomalous dimensions of higher spin currents…

The quasiconformal method provides us with a unified approach to the construction of minimal unitary representations (minrep) of noncompact groups, their deformations as well as their supersymmetric extensions. We review the quasiconformal…

The anomalous dimensions of planar N=4 SYM theory operators like tr(Phi D^S Phi) expanded in large spin S have the asymptotics \gamma= f ln S + f_c + 1/S (f_11 ln S + f_10) + ..., where f (the universal scaling function or cusp anomaly),…

By applying the stress-tensor-scalar operator product expansion (OPE) twice, we search for algebraic structures in $d=4$ conformal field theories (CFTs) with a pure Einstein gravity dual. We find that a rescaled mode operator defined by an…

In this paper, we elaborate on aspects of the recently introduced BMS bootstrap programme. We consider two-dimensional (2d) field theories with BMS3 symmetry and extensively use highest weight representations to uncover the BMS version of…

We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non--semi-simple associative algebras appearing in their lattice regularizations (as discussed in a companion…

The paper contributes to an ongoing effort to extend the conformal bootstrap beyond its traditional focus on systems of four-point correlation functions. Recently, it was demonstrated that semidefinite programming can be used to formulate a…

Bootstrap equations for conformal correlators that mimic the early theory of conformal bootstrap are written down in frames of the AdS/CFT approach. The simplified version of these equations, that may be justified if Schwinger-Keldysh…