Gauge bosons and the AdS_3/LCFT_2 correspondence

TL;DR

This paper investigates the relationship between gauge bosons and the AdS$_3$/LCFT$_2$ correspondence, finding that gauge bosons cannot be modeled within this specific holographic duality framework.

Contribution

It provides a detailed analysis of the singleton representation in AdS$_3$ and its connection to LCFT$_2$, demonstrating limitations of the AdS$_3$/LCFT$_2$ correspondence for gauge bosons.

Findings

The singleton can be expressed via dipole ghost fields coupled to boundary operators.

The calculated greybody factor matches bulk calculations in certain limits.

Gauge bosons are not realizable within the AdS$_3$/LCFT$_2$ correspondence.

Abstract

We study the relationship between the gauge boson coupled to spin 2 operator and the singleton in three-dimensional anti-de Sitter space(AdS$_3$). The singleton can be expressed in terms of a pair of dipole ghost fields $A$ and $B$ which couple to $D$ and $C$ operators on the boundary of AdS$_3$. These operators form the logarithmic conformal field theory(LCFT$_2$). Using the correlation function for logarithmic pair, we calculate the greybody factor for the singleton. In the low temperature limit of $\omega \gg T_{\pm}$, this is compared with the result of the bulk AdS$_3$ calculation of the gauge boson. We find that the gauge boson cannot be realized as a model of the AdS$_3$/LCFT$_2$ correspondence.