Instability in cosmological topologically massive gravity at the chiral point (0805.2610v4)

Abstract: We consider cosmological topologically massive gravity at the chiral point with positive sign of the Einstein-Hilbert term. We demonstrate the presence of a negative energy bulk mode that grows linearly in time. Unless there are physical reasons to discard this mode, this theory is unstable. To address this issue we prove that the mode is not pure gauge and that its negative energy is time-independent and finite. The isometry generators L_0 and \bar{L}_0 have non-unitary matrix representations like in logarithmic CFT. While the new mode obeys boundary conditions that are slightly weaker than the ones by Brown and Henneaux, its fall-off behavior is compatible with spacetime being asymptotically AdS_3. We employ holographic renormalization to show that the variational principle is well-defined. The corresponding Brown-York stress tensor is finite, traceless and conserved. Finally we address possibilities to eliminate the instability and prospects for chiral gravity.

• The paper identifies a negative energy bulk mode in CTMG at the chiral point, highlighting its potential to destabilize the gravitational framework.
• The analysis rigorously demonstrates that the mode is not a pure gauge and that the sign choice in the Einstein–Hilbert term critically affects BTZ black hole energies.
• The study applies holographic renormalization and explores LCFT connections, suggesting boundary adjustments as possible mitigations for the instability.

Analysis of Instability in Cosmological Topologically Massive Gravity at the Chiral Point

The paper by Daniel Grumiller and Niklas Johansson presents a detailed analysis of an instability in Cosmological Topologically Massive Gravity (CTMG) at the chiral point, often referred to as CCTMG. This work extends the understanding of gravitational theories in three dimensions, particularly exploring the inclusion of a gravitational Chern–Simons term in addition to the Einstein–Hilbert action with a negative cosmological constant.

Key Findings and Methodology

The authors explore the intricate structure of CTMG, notably focusing on its behavior at the chiral point, where the theories gravitate towards a specific set of conditions. They uncover a negative energy bulk mode, that grows linearly in time, presenting a potential source of instability unless conclusively dismissed on physical grounds. Importantly, the mode is shown not to be a pure gauge, ensuring its relevance and challenging the stability of the theory.

One notable aspect of the paper is the demonstration of how the Einstein–Hilbert term's sign choice affects the energy of the BTZ black hole and the massive graviton mode. The findings are substantiated by rigorous mathematical constructs, highlighting the role of the SL(2, R) × SL(2, R) isometry algebra and supporting the extension of Kraus and Larsen's holographic renormalization framework. The derived boundary stress tensor is finite, traceless, and conserved, positioning this work within the larger context of holographic principles and applications in AdS/CFT correspondence.

Implications of the Study

The identification of the non-unitary nature inherent in the theory via its link to logarithmic CFT (LCFT) brings about significant conceptual challenges. Particularly, the implications for the AdS/LCFT correspondence offer a fertile ground for further exploration in theoretical physics and the potential unification of gravity with quantum field theories.

The introduction of a negative energy mode raises fundamental questions about the theory's stability. The authors suggest that the instability might not be addressed through non-perturbative considerations alone, but also explore the possibility of consistent truncations or boundary condition adjustments that might mitigate the problem. However, the inherent non-unitarity tied to LCFT indicates that deeper alterations at both theoretical and quantum levels could be necessary for a stable, chiral gravitational theory.

Future Prospects

The future trajectory of research stemming from this paper involves several possibilities:

1. Truncation or Modification: Exploring boundary conditions or other modifications to feasibly exclude the destabilizing mode without altering the core properties of CCTMG could recast it as a viable chiral gravity theory.
2. Unitary Completion: Investigating pathways to integrate CCTMG within a broader framework that maintains unitarity could yield insights into a more robust gravitational theory.
3. LCFT Studies: Further investigation into the behaviors and properties of LCFTs, especially in three-dimensional contexts, can improve our understanding of non-unitary theories and their practical applications, potentially informing a broader context for gravity.

The paper emphasizes methodological rigor and comprehensive theoretical analysis, contributing valuable insights into the dynamics underpinning gravitational theories at the chiral point. As research continues, the exploration of these negative energy modes and their interactions within the cosmological frameworks will be crucial in advancing both theoretical physics and our understanding of fundamental gravitational phenomena.