Rank-n logarithmic conformal field theory in the BTZ black hole

TL;DR

This paper constructs a rank-$n$ finite temperature logarithmic conformal field theory (LCFT) in the BTZ black hole background, analyzing its correlation functions, quasinormal modes, and absorption cross section, revealing logarithmic corrections.

Contribution

It introduces a novel rank-$n$ finite temperature LCFT in the BTZ background and computes its two-point functions, quasinormal modes, and absorption features, extending previous lower-rank studies.

Findings

Derived all two-point functions of the rank-$n$ LCFT.

Calculated quasinormal modes from boundary Green's functions.

Identified $ ext{ln}^{n-1}[ ext{omega} ext{ell}]$-corrections in absorption cross section.

Abstract

We construct the rank-$n$ finite temperature logarithmic conformal field theory (LCFT) starting from the $n$-coupled scalar field theory in the BTZ black hole background. Its zero temperature limit reduces to a rank-$n$ LCFT in the AdS$_3$ background whose gravity dual is a polycritical gravity. We compute all two-point functions of a rank-$n$ finite temperature LCFT. Using the retarded Green's functions on the boundary, we obtain quasinormal modes of scalar $A_n$ which satisfies the $2n$-th order linearized equation. Furthermore, the absorption cross section of $A_n$ indicates a feature of $\ln^{n-1}[\omega \ell]$-correction to the Klein-Gordon mode.