Unitary Truncations and Critical Gravity: a Toy Model

TL;DR

This paper explores a higher-derivative scalar field model in AdS space as a simplified holographic dual to higher-rank logarithmic conformal field theories, revealing correlation functions and truncation properties.

Contribution

It introduces a toy model that reproduces higher-rank LCFT correlation functions holographically and discusses truncation in odd-rank cases for critical gravity implications.

Findings

Holographic two-point functions match higher-rank LCFT

Truncation to non-negative scalar product in odd-rank cases

Implications for higher-derivative critical gravity theories

Abstract

We investigate a higher-derivative scalar field model in a fixed d+1 dimensional AdS background as a toy model for a gravitational dual to a higher-rank logarithmic CFT. The holographic two-point correlation functions on the boundary agree with higher-rank LCFT correlation functions. For odd rank, the theory allows for a truncation to a nontrivial subspace with non-negative scalar product. We discuss possible implications for higher-derivative critical gravity theories.