String backgrounds and LCFT

TL;DR

This paper constructs a broad class of exact string backgrounds with null Killing vectors, leading to novel logarithmic conformal field theories (LCFTs), and provides explicit operator algebras and correlation functions for these models.

Contribution

It introduces a new class of LCFTs derived from coset models via a Penrose limit, with explicit operator algebra and background field expressions.

Findings

Derived exact operator algebra for basic chiral fields.

Computed four-point functions in the LCFTs.

Presented explicit background fields for specific models.

Abstract

We describe a large class of exact string backgrounds with a null Killing vector arising, via a limiting \`a la Penrose procedure, from string backgrounds corresponding to coset conformal field theories for compact groups G_N/H_N times a free time-like boson U(1)_{-N}. In this way a class of novel logarithmic conformal field theories (LCFT) emerges, that includes the one constructed recently as an N\to \infty limit of the SU(2)_N/U(1) X U(1)_{-N} theory. We explicitly give the exact operator algebra for the basic chiral fields as well as their representation in terms of free bosons, even though these are not known in general at finite N. We also compute four-point functions of various operators in the theory. For the cases of the four- and five-dimensional models, corresponding to a limit of the theory SO(D+1)_N/SO(D) X U(1)_{-N} for D=3 and 4, we also present the explicit expressions for the background fields.