A Yang-Mills model for centrally extended 2d gravity (original) (raw)

Yang-Mills model for centrally extended 2D gravity

Physical Review D, 2022

A Yang-Mills theory linear in the scalar curvature for 2d 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 rôle of the dilaton is played by the dual field strength of a U (1) gauge field. All vacuum solutions are found. They have constant scalar curvature and 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 CFT interpretation whose residual symmetry combines holomorphic diffeomorphisms with a subclass of U (1) gauge transformations while preserving dS 2 and AdS 2 boundary conditions. This is the same symmetry as in the Jackiw-Teitelboim-Maxwell 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.

Conformal and non-conformal symmetries in 2D dilaton gravity

Physics Letters B, 1997

We study finite-dimensional extra symmetries of generic 2D dilaton gravity models. Using a non-linear sigma model formulation we show that the unique theories admitting an extra (conformal) symmetry are the models with an ex-

Yang-Mills, Gravity, and 2D String Symmetries

It is well known that by using the innite dimensional symmetries that issue from string theories, one can build 2D geometric eld theories. These 2D eld theories can be identied with gravitational and gauge anomalies that arise in the presence of background gauge and gravitational anomalies. In this work we consider the background elds as residuum from reducing higher dimensional eld theories to two dimensions. This implies a new relationship between string theory and eld theories. We identify the isotropy equations of the distinct orbits as the Gau's law constraints of a Yang-Mills theory coupled to a gravitational theory that has been evaluated on a two-dimensional manifold. We show explicitly how one may recover the higher dimensional theories and extract this new theory of gravity and its coupling to Yang-Mills theory. This gravitational theory is able to couple to Yang-Mills via a torsion-like term and yet maintain gauge invariance. Also this new theory of gravity suggest a natural distinction between cosmology and local gravitation. We comment on the analogue of Chern-Simons theory for dieomorphism, the vacuum structure of gravity, and also the possibility of extracting explicit realizations of distinct dierentiable structures in four dimensions.

Conformal equivalence of 2D dilaton gravity models

Physics Letters B, 1997

We investigate the behavior of generic, matter-coupled, 2D dilaton gravity theories under dilaton-dependent Weyl rescalings of the metric. We show that physical observables associated with 2D black holes, such as the mass, the temperature and the flux of Hawking radiation are invariant under the action of both Weyl transformations and dilaton reparametrizations. The field theoretical and geometrical meaning of these invariances is discussed.

Generalized Yang-Mills theory and gravity

Physical Review D, 2016

We propose a generalization of Yang-Mills theory for which the symmetry algebra does not have to be factorized as mutually commuting algebras of a finite-dimensional Lie algebra and the algebra of functions on base space. The algebra of diffeomorphism can be constructed as an example, and a class of gravity theories can be interpreted as generalized Yang-Mills theories. These theories in general include a graviton, a dilaton and a rank-2 antisymmetric field, although Einstein gravity is also included as a special case. We present calculations suggesting that the connection in scattering amplitudes between Yang-Mills theory and gravity via BCJ duality can be made more manifest in this formulation.

A first-order approach to conformal gravity

Classical and Quantum Gravity, 2017

We investigate whether a spontaneously-broken gauge theory of the group SU (2, 2) may be a viable alternative to General Relativity. The basic ingredients of the theory are an SU (2, 2) gauge field A µ and a Higgs field W in the adjoint representation of the group with the Higgs field producing the symmetry breaking SU (2, 2) → SO(1, 3) × SO(1, 1). The action for gravity is polynomial in {A µ , W } and the field equations are first-order in derivatives of these fields. The new SO(1, 1) symmetry in the gravitational sector is interpreted in terms of an emergent local scale symmetry and the existence of 'conformalized' General Relativity and fourth-order Weyl conformal gravity as limits of the theory is demonstrated. Maximally symmetric spacetime solutions to the full theory are found and stability of the theory around these solutions is investigated; it is shown that regions of the theory's parameter space describe perturbations identical to that of General Relativity coupled to a massive scalar field and a massless one-form field. The coupling of gravity to matter is considered and it is shown that Lagrangians for all fields are naturally gauge-invariant, polynomial in fields and yield first-order field equations; no auxiliary fields are introduced. Familiar Yang-Mills and Klein-Gordon type Lagrangians are recovered on-shell in the General-Relativistic limit of the theory. In this formalism, the General-Relativistic limit coincides with a spontaneous breaking of scale invariance and it is shown that this generates mass terms for Higgs and spinor fields.

Constants of motion and the conformal anti-de Sitter algebra in (2+1)-Dimensional Gravity

International Journal of Modern Physics D

Constants of motion are calculated for 2+1 dimensional gravity with topology IR × T 2 and negative cosmological constant. Certain linear combinations of them satisfy the anti -de Sitter algebra so(2, 2) in either ADM or holonomy variables. Quantisation is straightforward in terms of the holonomy parameters. On inclusion of the Hamiltonian three new global constants are derived and the quantum algebra extends to that of the conformal algebra so(2, 3). The modular group appears as a discrete subgroup of the conformal group. Its quantum action is generated by these conserved quantities.

2D anti-de Sitter gravity as a conformally invariant mechanical system

Physical Review D, 2001

We show that two-dimensional (2D) AdS gravity induces on the spacetime boundary a conformally invariant dynamics that can be described in terms of a de Alfaro-Fubini-Furlan model coupled to an external source with conformal dimension two. The external source encodes the information about the gauge symmetries of the 2D gravity system. Alternatively, there exists a description in terms of a mechanical system with anholonomic constraints. The considered systems are invariant under the action of the conformal group generated by a Virasoro algebra, which occurs also as asymptotic symmetry algebra of two-dimensional anti-de Sitter space. We calculate the central charge of the algebra and find perfect agreement between statistical and thermodynamical entropy of AdS 2 black holes. *

Central charge for 2D gravity on AdS 2 and AdS 2 / CFT 1 correspondence

Journal of High Energy Physics, 2008

We study 2D Maxwell-dilaton gravity on AdS 2. We distinguish two distinctive cases depending on whether the AdS 2 solution can be lifted to an AdS 3 geometry. In both cases, in order to get a consistent boundary condition we need to work with a twisted energy momentum tensor which has non-zero central charge. With this central charge and the explicit form of the twisted Virasoro generators we compute the entropy of the system using the Cardy formula. The entropy is found to be the same as that obtained from gravity calculations for a specific value of the level of the U (1) current. The agreement is an indication of AdS 2 /CF T 1 correspondence.

Higher Gauge Theory and Gravity in 2+1 Dimensions

International Journal of Modern Physics A, 2007

Non-Abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher-dimensional (two-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-Abelian generalizations of the Yang–Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in 2+1 dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields — the ΣΦEA model — can be formulated as a higher gauge theory (as well as a standard gauge theory). Since the model has a very rich structure — it admits as solutions black...