Warped Conformal Field Theory (1210.0539v2)

Abstract: We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on right-movers. The local symmetries include one copy of the Virasoro algebra and a U(1) current algebra. This differs from the 2d conformal group, but in some respects is equally powerful in constraining the theory. In particular, the symmetries on a torus lead to modular covariance of the partition function, which is used to derive a universal formula for the asymptotic density of states. For an application we turn to the holographic description of black holes in quantum gravity, motivated by the fact that the symmetries in the near horizon geometry of any extremal black hole are identical to those of a 2d field theory with chiral scaling. We consider two examples: black holes in warped AdS_3 in topologically massive gravity, and in string theory. In both cases, the density of states in the 2d field theory reproduces the Bekenstein-Hawking entropy of black holes in the gravity theory.

• The paper introduces WCFTs as 2D quantum field theories with a single Virasoro algebra and a U(1) current that enforce strong symmetry constraints.
• It develops a novel modular transformation on a torus that computes the asymptotic density of states, bridging thermodynamics and field theory.
• The study applies WCFTs to holographic models of warped AdS3 black holes, successfully deriving black hole entropy in non-AdS contexts.

Overview of Warped Conformal Field Theory

The paper "Warped Conformal Field Theory" by Stéphane Detournay, Thomas Hartman, and Diego M. Hofman explores two-dimensional quantum field theories (QFTs) inheriting symmetries from both the Virasoro algebra and a U(1) Kac-Moody algebra, denoted as Warped Conformal Field Theories (WCFTs). These theories diverge from traditional conformal field theories (CFTs) by possessing a chiral scaling symmetry that operates solely on right-movers. The main focus is to elucidate the structure of WCFTs and demonstrate their connections to the holographic descriptions of black holes, particularly in non-AdS spacetimes.

Symmetries and Algebras

WCFTs are characterized by local symmetries extending SL(2;R) x U(1) into an infinite-dimensional algebra. The paper explores the intricacies of this symmetry, contrasting it with the dual Virasoro algebra in standard 2D CFTs. The authors outline a novel algebraic structure: a single Virasoro algebra supplemented by a U(1) current, crucial for describing the dynamics of WCFTs. The capacity of these symmetries to enforce stringent constraints on the field theory, analogous to those in CFTs, is highlighted, reinforcing the robust theoretical foundation of WCFTs.

Theoretical and Practical Implications

A significant implication of the research is the introduction of a new modular transformation specific to WCFTs on a toroidal geometry. This transformation parallels the role of modular invariance in CFTs, providing a universal formula for the asymptotic density of states. Importantly, the transformation links thermodynamic quantities under conditions of slow and high rotation, establishing an explicit relationship between the spectrum of a WCFT and other thermodynamic properties.

Holographic Applications

Applying the theoretical framework to gravitational contexts, the paper discusses black hole solutions in both warped AdS3 spacetimes within Topologically Massive Gravity (TMG) and string theory. In these scenarios, the authors demonstrate the derivation of black hole entropy using the asymptotic density of states from WCFT, thus matching the Bekenstein-Hawking entropy. This not only provides a novel computational approach but also enriches the understanding of WCFTs as relevant dual theories in holography, extending beyond asymptotically AdS spacetimes.

Future Developments

The work opens avenues for further exploration into the holographic correspondence in non-AdS and extremal black hole geometries, potentially expanding the applications of WCFTs. Consequently, this research might offer insights into higher-dimensional theories and their associated spacetime symmetries. The discussion of potential connections with higher-spin theories and modular properties of partition functions further underscores the potential of WCFTs to contribute to broader areas of theoretical physics.

Conclusion

Overall, this paper of Warped Conformal Field Theory makes substantial contributions to theoretical physics by expanding the landscape of applicable field theories and their holographic duals. By providing both theoretical insights and practical results for black hole entropy, the paper sets a foundation for future investigations into non-standard conformal symmetries and their implications in quantum gravity. The continued exploration of WCFTs is poised to inform not only spacetime symmetries but the intricacies of duality principles in modern theoretical frameworks.