On the conformal transformation and duality in gravity
نویسنده
چکیده
The theory described by the sum of the Einstein-Hilbert action and the action of conformal scalar field possesses the duality symmetry which includes some special conformal transformation of the metric, and also inversion of scalar field and of the gravitational constant. In the present paper the conformal duality is generalized for an arbitrary space-time dimension n 6= 2 and for the general sigma-model type conformal scalar theory. We also consider to apply the conformal duality for the investigation of quantum gravity in the strong curvature regime. The trace of the first coefficient of the Schwinger-DeWitt expansion is derived and it’s dependence on the gauge fixing condition is considered. After that we discuss the way to extract the gauge-fixing independent result and also it’s possible physical applications. Introduction It is well known that the study in the field of quantum gravity meets serious difficulties. On classical level General Relativity is in a good accordance with all the known tests, but quantum theory based on GR is nonrenormalizable [1]. Indeed there are a number of approaches to investigate some aspects of quantum gravitational phenomenons. One can mention the idea of inducing GR from the quantum effects of matter fields or from the theory of string (see, for example, [2] and [3]). Recently there were a very interesting attempts to extract the low-energy predictions from the GRbased quantum theory of gravity [4, 5]. However the principal problem with the lack of quantum gravitational experiments doesn’t enable one to choose among the numerous theories and therefore the models for quantum gravity are subjects of wide arbitrariness. This concerns, for instance, the choice of the model for the description of low-energy quantum gravitational phenomena, where the string-inspired action contains, along with the metric, massless dilaton field. In such a situation a lot of attention has been attracted by the models which have more symmetries than GR. In particular, one can mention the supergravity theories, and also the theories with local conformal invariance. The conformal transformation and conformal symmetry in gravity are especially interesting in many respects [6, 7] because of their relation with the cosmological applications [8] and with the On leave from Tomsk Pedagogical University, 634041, Tomsk, Russia E-mail: [email protected]
منابع مشابه
تبدیلات دوگانگی آبلی استاندارد در گرانش f(T)
According to the perturbation order, the equations of motion of low-energy string effective action are the generalized Einstein equations. Thus, by making use of the conformal transformation of the metric tensor, it is possible to map the low-energy string effective action into f(T) gravity, relating the dilaton field to the torsion scalar. Considering a homogeneous and isotropic universe and ...
متن کاملv 1 2 8 M ay 1 99 9 A new conformal duality of spherically symmetric space – times
A contribution linear in r to the gravitational potential can be created by a suitable conformal duality transformation: the conformal factor is 1/(1 + r) and r will be replaced by r/(1 + r), where r is the Schwarzschild radial coordinate. Thus, every spherically symmetric solution of conformal Weyl gravity is conformally related to an Einstein space. This result finally resolves a long controv...
متن کاملOn conformal transformation of special curvature of Kropina metrics
An important class of Finsler metric is named Kropina metrics which is defined by Riemannian metric α and 1-form β which have many applications in physic, magnetic field and dynamic systems. In this paper, conformal transformations of χ-curvature and H-curvature of Kropina metrics are studied and the conditions that preserve this quantities are investigated. Also it is shown that in the ...
متن کاملOn Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric
Let be an n-dimensional Riemannian manifold, and be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation induces an infinitesimal homothetic transformation on . Furthermore, the correspondence gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on onto the Lie algebra of infinitesimal ...
متن کاملWhat can gauge-gravity duality teach us about condensed matter physics?
I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two spatial dimensions, which display quantum critical points described by conformal field theories. Questions associated with non-zero temperature dynamics and trans...
متن کامل