Abstract

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 higherderivative critical gravity theories.

Highlights

  • New Massive Gravity instead can be formulated in dimensions higher than three

  • On the dual field theory side this means that there should exist a consistent truncation of the LCFT that leads to an ordinary CFT

  • We calculate two-point correlation functions on the boundary and we show that these agree with the rank r LCFT two-point correlators

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Summary

A scalar field dual of a rank r LCFT

We propose a scalar field model dual to a rank r LCFT. We proceed to calculate the scalar product in the bulk and we point out the existence of a nontrivial subspace for odd rank with positive definite inner product. The equations of motion and the on-shell action are invariant under a shift of the scalar fields by: i−1 φi → φi + λkφi−k k=1. We assume that the scalar field configuration decouples from the metric equations of motions at least up to the order of coefficients that contribute to any divergent terms in the bulk action. This assumption justifies ignoring the back reaction of the scalars on the metric

From r degenerate masses to a rank r LCFT
Comparison with known results
A non-negative scalar product
A special case: the singleton
Discussion
A Normalization of the two-point functions
Near-boundary expansion
Normalization of the holographic 2-pt correlation functions
Full Text
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