Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields (1008.4744v2)

Abstract: We discuss the emergence of W-algebras as asymptotic symmetries of higher-spin gauge theories coupled to three-dimensional Einstein gravity with a negative cosmological constant. We focus on models involving a finite number of bosonic higher-spin fields, and especially on the example provided by the coupling of a spin-3 field to gravity. It is described by a SL(3) \times SL(3) Chern-Simons theory and its asymptotic symmetry algebra is given by two copies of the classical W_3-algebra with central charge the one computed by Brown and Henneaux in pure gravity with negative cosmological constant.

• The paper extends three-dimensional gravity by coupling spin-3 fields via a Chern-Simons formulation, enabling new boundary dynamics.
• It identifies emergent W-algebra symmetries that match Brown-Henneaux central charges, confirming consistency with pure gravity results.
• The model opens potential for extending the AdS/CFT correspondence to include higher-spin theories and novel conformal structures.

Analysis of Asymptotic Symmetries in Three-Dimensional Gravity with Higher-Spin Couplings

The paper "Asymptotic Symmetries of Three-Dimensional Gravity Coupled to Higher-Spin Fields" addresses the complex problem of integrating higher-spin fields into gravitational systems while examining their asymptotic symmetries in a three-dimensional context with a negative cosmological constant. The authors focus on constructing models grounded in Chern-Simons theory characterized by finite-dimensional gauge groups, extending the well-studied asymptotic conformal symmetries found in three-dimensional Einstein gravity to settings where higher-spin fields are present.

Key Features

1. Higher-Spin Coupling in Three Dimensions: The paper builds upon the peculiarities of three-dimensional spacetime where massless higher-spin fields intrinsically do not carry local degrees of freedom. By coupling these fields to gravity, additional boundary dynamics can be explored without introducing the propagation issues typical in higher dimensions.
2. Chern-Simons Formulation: The integration of higher-spin fields into gravity is framed via a Chern-Simons action. The paper elucidates an SL(3) × SL(3) model enabling the description of a spin-3 field coupled to gravity. This model serves as a particular embodiment of a larger class characterized by SL(n) × SL(n) gauge groups, which realize a hierarchy of integer spins.
3. Asymptotic Symmetries and W-Algebras: Central to the paper is the identification of W-algebras as governing asymptotic symmetries. For the SL(3) case, the emergent symmetry is a W₃ ⊗ W₃ algebra possessing central charges consistent with the Brown-Henneaux result for pure gravity. This symmetry extends the conformal algebras and offers new insights into the dynamics at the spacetime boundary.

Implications and Theoretical Insights

The research explores the implications of integrating higher-spin symmetries in a three-dimensional gravity context. The establishment of a Chern-Simons framework enables the seamless incorporation of spin-3 fields without the complications arising in higher-dimensional analogs. Crucially, the asymptotic symmetry analysis opens avenues for extending the AdS/CFT correspondence to higher-spin theories, where W-algebras play a significant role in the boundary field theoretical description.

Numerical and Structural Claims

The paper reveals that the central charge determined from the asymptotic analysis matches Brown and Henneaux's in pure gravity, reinforcing the robustness of the proposed higher-spin model. The potential to reproduce consistent conformal symmetry scenarios offers validation for choosing Chern-Simons actions as natural settings for these studies.

Speculations on Future Research

The findings propose potential pathways for extending the AdS/CFT framework, particularly using Toda theories at the conformal boundary. Further exploration into open string theories and higher dimensions, as well as supergravity extensions with inclusion of fermions, could provide more comprehensive models. In-depth examination of gauge symmetries, including possible non-principal embeddings and Chan-Paton factors, is likely to yield richer frameworks and identify new theoretical patterns.

In summary, this paper constructs a detailed narrative framing higher-spin field interactions within a gravitational context in three dimensions, focusing on Chern-Simons formulations and their corresponding asymptotic symmetries. As the field progresses, these models provide a scaffold for future exploration in advanced gravitational theories and quantum gravity correspondence.