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Short-cut to new anomalies in gravity duals to logarithmic conformal field theories

Daniel Grumiller, Niklas Johansson, Thomas Zojer

TL;DR

The work investigates gravity duals of logarithmic conformal field theories in three dimensions, focusing on TMG, NMG, GMG, and PMG. It introduces a general short-cut to extract LCFT new anomalies $b_L$ (and $b_R$) from degenerations of operator weights in parameterized CFT families and demonstrates its validity on known cases. Applying the method to GMG yields explicit formulas for rank-2 standard, rank-3 standard, and rank-2 exotic regimes, revealing a rich LCFT structure including possible rank-3 Jordan cells. The analysis of PMG provides compelling evidence for a negative-central-charge LCFT dual with a rank-2 Jordan cell, while generalisations to higher-derivative theories with holographic $c$-theorems are discussed as promising avenues for future work.

Abstract

Various massive gravity theories in three dimensions are conjecturally dual to logarithmic conformal field theories (LCFTs). We summarise the status of these conjectures. LCFTs are characterised by the values of the central charges and the so-called "new anomalies". We employ a short-cut to calculate these new anomalies in generalised massive gravity and in the recently proposed higher-derivative gravity theories with holographic c-theorem. Both cases permit LCFTs exhibiting intriguing features, like rank three Jordan cells or non-zero central charges. Finally, as an example we discuss in some detail the partially massless version of new massive gravity, a theory with several special properties that we call "partially massless gravity".

Short-cut to new anomalies in gravity duals to logarithmic conformal field theories

TL;DR

The work investigates gravity duals of logarithmic conformal field theories in three dimensions, focusing on TMG, NMG, GMG, and PMG. It introduces a general short-cut to extract LCFT new anomalies (and ) from degenerations of operator weights in parameterized CFT families and demonstrates its validity on known cases. Applying the method to GMG yields explicit formulas for rank-2 standard, rank-3 standard, and rank-2 exotic regimes, revealing a rich LCFT structure including possible rank-3 Jordan cells. The analysis of PMG provides compelling evidence for a negative-central-charge LCFT dual with a rank-2 Jordan cell, while generalisations to higher-derivative theories with holographic -theorems are discussed as promising avenues for future work.

Abstract

Various massive gravity theories in three dimensions are conjecturally dual to logarithmic conformal field theories (LCFTs). We summarise the status of these conjectures. LCFTs are characterised by the values of the central charges and the so-called "new anomalies". We employ a short-cut to calculate these new anomalies in generalised massive gravity and in the recently proposed higher-derivative gravity theories with holographic c-theorem. Both cases permit LCFTs exhibiting intriguing features, like rank three Jordan cells or non-zero central charges. Finally, as an example we discuss in some detail the partially massless version of new massive gravity, a theory with several special properties that we call "partially massless gravity".

Paper Structure

This paper contains 20 sections, 83 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Confirmations of LCFT conjecture for TMG
  3. Early indications
  4. Correlators and 1-loop partition function
  5. LCFT conjecture for other massive gravity theories
  6. New massive gravity
  7. Generalised massive gravity
  8. Short-cut to new anomalies
  9. Introducing the short-cut
  10. Known examples
  11. New anomalies in generalised massive gravity
  12. New anomalies in generalised massive gravity
  13. Rank 2 standard case: $m_1 \ell = 1$
  14. Rank 3 standard case: $m_1 \ell = m_2 \ell = 1$
  15. Rank 2 exotic case: $m_1 \ell = m_2 \ell \neq 1$
  16. ...and 5 more sections

Figures (3)

  • Figure 1: Real (a) and imaginary (b) parts of $\ln Z_{\rm TMG}^{\rm 1-loop}$. The shading goes from darker (lower values) to brighter (higher values). The plots are cut off at large positive and negative values, so the white regions along the unit circle represent poles of either sign.
  • Figure 2: Special loci in the GMG parameter space. See main text for explanations.
  • Figure 3: Display of the ladder operators $L_+$ (up), $L_-$ (down), $\bar{L}_+$ (right) and $\bar{L}_-$ (left). Notation: $\odot=$ primaries, $\bullet=$ descendants, $\circ=$ other, $\dots=$ semi-permeable barrier.