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Holographic applications of logarithmic conformal field theories

D. Grumiller, W. Riedler, J. Rosseel, T. Zojer

TL;DR

This review surveys how Jordan cells and logarithmic conformal field theories arise in holography, centering on AdS3/log CFT2 and the family of critical gravity theories (TMG, NMG, GMG, PET) that generate log modes. It compiles checks from gravity computations (correlators, Ward identities, partition functions) and maps them to log CFT expectations, highlighting the role of the new anomaly b_L and the formation of Jordan cells. The article then expands to supersymmetric extensions, higher dimensions, and generalized spins/backgrounds, and discusses Inonu–Wigner contractions to log Galilean algebras and potential condensed-matter applications. It closes with a discussion of missing checks and open issues such as entanglement entropy, transport, and possible string-theoretic embeddings. Overall, the work charts the landscape of AdS/log CFT dualities, clarifying where evidence is strongest and where further work is needed to solidify these non-unitary holographic correspondences.

Abstract

We review the relations between Jordan cells in various branches of physics, ranging from quantum mechanics to massive gravity theories. Our main focus is on holographic correspondences between critically tuned gravity theories in Anti-de Sitter space and logarithmic conformal field theories in various dimensions. We summarize the developments in the past five years, include some novel generalizations and provide an outlook on possible future developments.

Holographic applications of logarithmic conformal field theories

TL;DR

This review surveys how Jordan cells and logarithmic conformal field theories arise in holography, centering on AdS3/log CFT2 and the family of critical gravity theories (TMG, NMG, GMG, PET) that generate log modes. It compiles checks from gravity computations (correlators, Ward identities, partition functions) and maps them to log CFT expectations, highlighting the role of the new anomaly b_L and the formation of Jordan cells. The article then expands to supersymmetric extensions, higher dimensions, and generalized spins/backgrounds, and discusses Inonu–Wigner contractions to log Galilean algebras and potential condensed-matter applications. It closes with a discussion of missing checks and open issues such as entanglement entropy, transport, and possible string-theoretic embeddings. Overall, the work charts the landscape of AdS/log CFT dualities, clarifying where evidence is strongest and where further work is needed to solidify these non-unitary holographic correspondences.

Abstract

We review the relations between Jordan cells in various branches of physics, ranging from quantum mechanics to massive gravity theories. Our main focus is on holographic correspondences between critically tuned gravity theories in Anti-de Sitter space and logarithmic conformal field theories in various dimensions. We summarize the developments in the past five years, include some novel generalizations and provide an outlook on possible future developments.

Paper Structure

This paper contains 21 sections, 98 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Jordan cells in quantum mechanics
  3. Log CFT basics
  4. AdS$_3$/CFT$_2$ crash course
  5. AdS$_3$/log CFT$_2$ correspondence
  6. Critical TMG --- chiral or log?
  7. Checks and features of the correspondence
  8. Jordan cells in other higher-derivative gravity theories
  9. New massive gravity
  10. Generalized massive gravity
  11. Parity-even tricritical gravity
  12. More critical models in three dimensions
  13. Generalizations
  14. Supersymmetry
  15. Generalization to higher dimensions, AdS$_{d+1}$/log CFT$_{d}$
  16. ...and 6 more sections

Figures (1)

  • Figure 1: Special loci in the GMG parameter space. See main text for explanations.