Singletons and Logarithmic CFT in ADS/CFT correspondence

TL;DR

This paper explores the connection between singleton fields in AdS space and logarithmic conformal field theories at the boundary, revealing how bulk dynamics induce logarithmic correlations on the boundary.

Contribution

It demonstrates that singleton fields in AdS induce logarithmic two-point functions on the boundary, providing a bulk interpretation of logarithmic operator mixing.

Findings

Singleton bulk Lagrangian induces logarithmic correlators at the boundary

Bulk interpretation of operator mixing under scale transformations

Establishes a link between bulk singletons and boundary logarithmic CFTs

Abstract

We discuss a possible relation between singletons in $AdS$ space and logarithmic conformal field theories at the boundary of $AdS$. It is shown that the bulk Lagrangian for singleton field (singleton dipole) induces on the boundary the two-point correlation function for logarithmic pair. Bulk interpretation of mixing between logarithmic operator $D$ and zero mode operator $C$ under the scale transformation is discussed as well as some other issues.