New method for the conformal bootstrap with OPE truncations

Abstract

We investigate two aspects of conformal field theories. In the first part, we study the general 4-point correlator of identical scalars around the fully crossing symmetric point $u=v=1$, where $u,v$ are conformally invariant cross ratios. Since this point is fully crossing invariant, we can deduce some general properties of the 4-point correlators from crossing symmetry. In the second part, we discuss the conformal bootstrap with OPE truncations. As a generalization of Gliozzi's method, we propose to extract the low-lying CFT data by minimizing the "error" induced by an OPE truncation. The error function $\eta$ measures the violation of crossing symmetry. The geometric interpretation of $\eta$ is the length of the vector associated with the truncated OPE. As an example, we apply the error-minimization method to the 2d Ising CFT with severely truncated OPEs.

17 pages, 1 figure; v2: typos fixed, references added; v3: 19 pages, 1 figure, typos fixed, references added, improvements made, error estimations added

References in corpus (14)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Bounds in 4D Conformal Field Theories with Global Symmetry
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• A Semidefinite Program Solver for the Conformal Bootstrap
• JuliBootS: a hands-on guide to the conformal bootstrap
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
• Inverse Bootstrapping Conformal Field Theories
• Modular Bootstrap Revisited
• ${\varphi }^3$ theory with $F_4$ flavor symmetry in $6-2\epsilon$ dimensions: 3-loop renormalization and conformal bootstrap