Logarithmic conformal field theories and AdS correspondence

TL;DR

The paper extends the AdS/CFT correspondence to logarithmic conformal field theories (LCFTs) by formulating a two-scalar AdS action that, upon projecting to the boundary, yields LCFT operators. It demonstrates that the boundary operator $\mathcal O'$ behaves as the $\Delta$-derivative of the ordinary boundary operator $\mathcal O$, producing a Jordan-block structure and logarithmic two-point functions. Through the introduction of interactions, it derives general tree-level $n$-point functions where logarithmic terms appear in correlators involving $\mathcal O'$, and shows that these LCFT correlators can be obtained by differentiating ordinary CFT correlators with respect to the conformal weight $\Delta$. The work provides a systematic holographic framework to generate LCFT data from AdS theories, enabling explicit calculations of LCFT correlators via weight-derivative operations.

Abstract

We generalize the Maldacena correspondence to the logarithmic conformal field theories. We study the correspondence between field theories in (d+1)-dimensional AdS space and the d-dimensional logarithmic conformal field theories in the boundary of $AdS_{d+1}$. Using this correspondence, we get the n-point functions of the corresponding logarithmic conformal field theory in d-dimensions.