PP-waves and logarithmic conformal field theories

TL;DR

This paper interprets the plane wave limit of certain supergravity backgrounds using logarithmic conformal field theories, providing explicit examples and computations that connect classical and quantum descriptions.

Contribution

It introduces a novel logarithmic conformal field theory derived from a contraction of a coset model, with detailed quantum and classical analysis.

Findings

Derived a new logarithmic CFT with central charge c=3

Computed four-point functions involving logarithmic partners

Constructed an infinite set of logarithmic operators using extended symmetries

Abstract

We provide a world-sheet interpretation to the plane wave limit of a large class of exact supergravity backgrounds in terms of logarithmic conformal field theories. As an illustrative example, we consider the two-dimensional conformal field theory of the coset model SU(2)_N/U(1) times a free time-like boson U(1)_{-N}, which admits a space-time interpretation as a three-dimensional plane wave solution by taking a correlated limit \`a la Penrose. We show that upon a contraction of Saletan type, in which the parafermions of the compact coset model are combined with the free time-like boson, one obtains a novel logarithmic conformal field theory with central charge c=3. Our results are motivated at the classical level using Poisson brackets of the fields, but they are also explicitly demonstrated at the quantum level using exact operator product expansions. We perform several computations in this theory including the evaluation of the four-point functions involving primary fields and their logarithmic partners, which are identified. We also employ the extended conformal symmetries of the model to construct an infinite number of logarithmic operators. This analysis can be easily generalized to other exact conformal field theory backgrounds with a plane wave limit in the target space.