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

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• The unitary subsector of generalized minimal models
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• Ising model close to $d=2$
• Lightcone expansions of conformal blocks in closed form
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• Conformal Bootstrap Deformations
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• Crossing, Modular Averages and $N\leftrightarrow k$ in WZW Models