Analytic Bootstrap for Logarithmic CFT

TL;DR

This paper applies conformal bootstrap methods to four-dimensional logarithmic conformal field theories, deriving constraints on operator dimensions and energies, and confirming the cluster decomposition principle for positive operator dimensions.

Contribution

It introduces a bootstrap approach to LogCFTs in four dimensions, computing anomalous dimensions and energy shifts for large spin operators, and explores holographic duals involving higher derivatives.

Findings

Anomalous dimensions of double trace operators computed in LogCFTs.

Energy shifts related to holographic duals match bootstrap predictions.

Cluster decomposition principle holds for positive operator dimensions.

Abstract

We study logarithmic conformal field theory (LogCFT) in four dimensions using conformal bootstrap techniques in the large spin limit. We focus on the constraints imposed by conformal symmetry on the four point function of certain logarithmic scalar operators and compute the leading correction to the anomalous dimension of double trace operators in the large spin limit. There exist certain holographic duals to such LogCFTs, which involve higher derivative equations of motion. The anomalous dimension is related to the binding energy of a state where two scalars rotate around each other with a large angular momentum. We compute this energy shift and compare it to the anomalous dimension of the large spin double trace operators due to stress tensor exchange in the LogCFT. Our result shows that the cluster decomposition principle is satisfied for LogCFTs as long as the dimensions of the operators are positive.