Abstract
A Yang-Mills theory linear in the scalar curvature for two-dimensional gravity with symmetry generated by the semidirect product formed with the Lie derivative of the algebra of diffeomorphisms with the two-dimensional Abelian algebra is formulated. As compared with dilaton models, the role of the dilaton is played by the dual field strength of a $U(1)$ gauge field. All vacuum solutions are found. They are either black holes or have constant scalar curvature. Those with constant scalar curvature have constant dual field strength. In particular, solutions with vanishing cosmological constant but nonzero scalar curvature exist. In the conformal-Lorenz gauge, the model has a conformal field theory interpretation whose residual symmetry combines holomorphic diffeomorphisms with a subclass of $U(1)$ gauge transformations while preserving two-dimensional de Sitter and anti-de Sitter boundary conditions. This is the same symmetry as in Jackiw-Teitelboim-Maxwell gravity considered by Hartman and Strominger. It is argued that this is the only nontrivial Yang-Mills model linear in the scalar curvature that exists for real Lie algebras of dimension four.
Highlights
Two-dimensional (2D) dilaton gravity models provide effective theories to study regimes of interest in higherdimensional gravity
Among them are Jackiw-Teitelboim (JT) gravity [1,2], with a linear coupling φR between the dilaton and the scalar curvature and which accounts for near-horizon theories in higher-dimensional near-extremal black holes; the Almheiri-Polchinski [3] models, with quadratic coupling φ2R, that consistently explain the holographic flow to AdS2 × X of many theories; and the Callan-Giddings-Harvey-Strominger model [4], with exponential coupling e−φR, that provides a 2D setting to analytically understand the formation and subsequent evaporation of a black hole
We propose a nondilaton model in which the role of the dilaton is played by the dual field strength ÃF of an Abelian gauge field Aμ
Summary
Two-dimensional (2D) dilaton gravity models provide effective theories to study regimes of interest in higherdimensional gravity. Among them are Jackiw-Teitelboim (JT) gravity [1,2], with a linear coupling φR between the dilaton and the scalar curvature and which accounts for near-horizon theories in higher-dimensional near-extremal black holes; the Almheiri-Polchinski [3] models, with quadratic coupling φ2R, that consistently explain the holographic flow to AdS2 × X of many theories; and the Callan-Giddings-Harvey-Strominger model [4], with exponential coupling e−φR, that provides a 2D setting to analytically understand the formation and subsequent evaporation of a black hole. We propose a nondilaton model in which the role of the dilaton is played by the dual field strength ÃF of an Abelian gauge field Aμ.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
