Massive Gravity in Three Dimensions (0901.1766v3)

Abstract: A particular higher-derivative extension of the Einstein-Hilbert action in three spacetime dimensions is shown to be equivalent at the linearized level to the (unitary) Pauli-Fierz action for a massive spin-2 field. A more general model, which also includes topologically-massive' gravity as a special case, propagates the two spin 2 helicity states with different masses. We discuss the extension to massive ${\cal N}$-extended supergravity, and we present acosmological' extension that admits an anti-de Sitter vacuum.

• The paper introduces a higher-derivative extension to 3D gravity that achieves a unitary theory with massive spin-2 modes equivalent to the Pauli–Fierz formulation.
• It employs a triple-master action to unify different 3D massive gravity models, bridging connections between topologically massive gravity and new massive gravity.
• The study explores cosmological and supersymmetric extensions, offering insights into quantum gravity in lower dimensions with implications for anti-de Sitter vacua and UV finiteness.

Overview of "Massive Gravity in Three Dimensions"

The paper "Massive Gravity in Three Dimensions" by Eric A. Bergshoeff, Olaf Hohm, and Paul K. Townsend explores the theoretical development of a higher-derivative extension of the Einstein-Hilbert action in three spacetime dimensions. This work reveals crucial relationships between various theories of gravity and their implications for three-dimensional (3D) physics, particularly focusing on the unitarity and massiveness of graviton modes.

Theoretical Framework

The authors propose a novel approach by extending the Einstein-Hilbert action with higher-derivative terms. They demonstrate that this extended action is equivalent to the linearized Pauli-Fierz action for a massive spin-2 field, thus ensuring unitary propagation of massive gravitons in 3D, which is a notable divergence from traditional four-dimensional (4D) general relativity. Notably, unlike the 4D case, which presents challenges of non-unitarity in higher-derivative theories, their 3D model achieves unitarity and renormalizability, leading to super-renormalizability due to the lower dimensionality.

Key Contributions and Findings

1. Massive Gravity Theory in 3D: The paper introduces a parity-preserving variant of 3D gravity, which, when quantized, yields a unitary interacting graviton theory with two polarization states of helicities ±2. The field equations are fourth-order in derivatives, but linearization reveals equivalency with a free Pauli-Fierz theory in 3D.
2. Master Action Formalism: They present a "triple-master" action unifying various 3D massive gravity theories. This action bridges connections between topologically massive gravity (TMG) and their new massive gravity (NMG), highlighting the theoretical equivalence and differences in propagating modes.
3. Cosmological and Supersymmetric Extensions: The investigation extends to cosmological versions allowing anti-de Sitter (adS) vacua. The authors also touch upon extensions into N-extended supergravity, hinting at possible supersymmetric models that could provide ultra-violet (UV) finiteness, akin to some 4D supersymmetric theories.
4. Comparison with TMG: By establishing connections with TMG through linearization of their newly proposed equations, the authors show that TMG can be viewed as a "square-root" of their massive gravity formulation, offering a fresh perspective on how parity violations can be systematically studied within the 3D framework.

Practical and Theoretical Implications

The insights from this paper have profound implications for understanding gravity in lower dimensions. By proving unitary propagation of massive gravitons, this model provides a potential platform for exploring quantum gravity in a simplified setting without encountering the non-renormalizability issues of higher dimensions. The theoretical equivalences and extensions discussed can inform further research in supergravity and quantum cosmology, potentially leading to a deeper grasp of gravity's role in various dimensional settings.

Speculation on Future Developments

The work presented invites further inquiry into supersymmetry's role in lower-dimensional gravity theories. Exploring N=4 supergravity extensions, as conjectured by the authors, could yield finite models, offering greater insights into the holographic principle and the nature of spacetime itself. Additionally, the creation of new models based on the "general massive gravity" framework could stimulate advances in understanding black hole thermodynamics within 3D settings, particularly in relation to the BTZ black holes and their microscopics.

In conclusion, the theoretical constructs and analyses laid out in this paper provide a comprehensive framework for a deeper understanding of 3D gravity and its implications for broader gravitational theories. Researchers in the field are encouraged to explore the ramifications and extensions of these findings in the context of both classical and quantum gravity.