We analyse boundary conformal field theories on random surfaces using the conformal gauge approach of David, Distler and Kawai. The crucial point is the choice of boundary conditions on the Liouville field. We discuss the Weyl anomaly cancellation for Polyakov’s non-critical open bosonic string with Neumann, Dirichlet and free boundary conditions. Dirichlet boundary conditions on the Liouville ...

According to the Maupertuis principle, the movement of a classical particle in an external potential V (x) can be understood as the movement in a curved space with the metric gμν(x) = 2M [V (x) − E]δμν . We show that the principle can be extended to the quantum regime, i.e., we show that the wave function of the particle follows a Schrödinger equation in curved space where the kinetic operator ...

We study the vacuum, plane-wave Bianchi V IIh spacetimes described by the Lukash metric. By combining covariant with orthonormal frame techniques, we describe these models in terms of their irreducible kinematical and geometrical quantities. This covariant description is used to study analytically the response of the Lukash spacetime to linear perturbations. We find that the stability of the va...

Let M be a four-dimensional orientable manifold equipped with a Minkowski type metric g and with a polarization. In general relativity such a manifoldM is used as a stage for all physical phenomena. When describing the spin phenomenon M is additionally assumed to be a spin manifold. In this case it admits two spinor bundles: the bundle of Weyl spinors SM and the bundle of Dirac spinors DM (see ...

We perform the spherical symmetric dimensional reduction 4d → 2d of heterotic string theory. We find a class of two-dimensional (2d) dilaton gravity models that gives a general description of the near-horizon, near-extremal behavior of four-dimensional (4d) heterotic string black holes. We show that the duality group of the 4d theory is realized in two dimensions in terms of Weyl transformation...

Abstract We consider a Weyl–Lorentz- U (1)-invariant gravity model written in terms of scalar field, electromagnetic field and nonmetricity without torsion curvature, the so-called symmetric teleparallel geometry, three dimensions. Firstly, we obtain variational equations from Lagrangian. Then, find some classes circularly rotating solutions by making only metric ansatz. The coincident gauge sp...

We perform the spherical symmetric dimensional reduction 4d → 2d of heterotic string theory. We find a class of two-dimensional (2d) dilaton gravity models that gives a general description of the near-horizon, near-extremal behavior of four-dimensional (4d) heterotic string black holes. We show that the duality group of the 4d theory is realized in two dimensions in terms of Weyl transformation...

The dynamical evolution of internal space-like dimensions breaks the invariance of the Maxwell’s equations under Weyl rescaling of the (conformally flat) four-dimensional metric. Depending upon the number and upon the dynamics of internal dimensions large scale magnetic fields can be created. The requirements coming from magnetogenesis together with the other cosmological constraints are examin...

The necessary and sufficient condition for the existence of αsurfaces in complex space-time manifolds with nonvanishing torsion is derived. For these manifolds, Lie brackets of vector fields and spinor Ricci identities contain explicitly the effects of torsion. This leads to an integrability condition for α-surfaces which does not involve just the self-dual Weyl spinor, as in complexified gener...

The three 3-brane system with both positive or negative tension is studied in a low energy regime by using gradient expansion method. The effective equations of motion on the brane is derived and in particular we examine, in the first order, the radion effective lagrangian for this system. In this case, we show the solution of the modified Friedmann equation with dark radiation on the middle br...