We study geometry of two-dimensional models of conformal spacetime based on the group of Möbius transformation. The natural geometric invariants, called cycles, are used to linearise Möbius action. Conformal completion of the space-time is achieved through an addition of a zero-radius cycle at infinity. We pay an attention to the natural condition of non-reversibility of time arrow in order to ...

Using the conformal compensator superfields of N=2 D=4 supergravity, the Type IIB S-duality transformations are expressed as a linear rotation which mixes the compensator and matter superfields. The classical superspace action for D = 4 compactifications of Type IIB supergravity is manifestly invariant under this transformation. Furthermore, the introduction of conformal compensators allows a F...

Recall the global U(1) symmetry: Ψ→ e−ieΨ i.e. δΨ = −ieΨ. Let’s run the Noether argument: consider a slightly deformed, infinitesimal version of the symmetry transformation: Ψ→ Ψ + ρδΨ, where is just a small number to keep track of order, and ρ is some general function of x. The fact that we have a U(1) symmetry tells us the action must change under the deformed transformation by δS = ∫ dx J N∂...

We deal with a 2m-dimensional Riemannian manifold (M,g) structured by an affine connection and a vector field , defining a -parallel connection. It is proved that is both a torse forming vector field and an exterior concurrent vector field. Properties of the curvature 2-forms are established. It is shown that M is endowed with a conformal symplectic structure Ω and defines a relative conformal ...

The initial-value problem is posed by giving a conformal three-metric on each of two nearby spacelike hypersurfaces, their proper-time separation up to a multiplier to be determined, and the mean (extrinsic) curvature of one slice. The resulting equations have the same elliptic form as does the one-hypersurface formulation. The metrical roots of this form are revealed by a conformal " thin sand...

The technique of Darboux transformation is applied to nonlocal partner of two– dimensional periodic An−1 Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with quantized spectral parameter. The generalization of the Darboux transformation technique on linear equations of such a kind is given. The connect...

Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local free field theories. Physical applications include uniaxial Lifshitz points and ageing in simple ferromagnets. Scale invariance is a central notion of moder...

We answer a question raised by M. Chuaqui, P. Duren, and B. Osgood by showing that a conformal mapping of a simply connected domain cannot take two circles onto two proper ellipses. The goal of this note is to prove the following. Proposition 1. Let Ω be a simply connected domain on C = C ∪ {∞} containing circles (on C) C1 and C2, C1 = C2. Let f be a conformal mapping from Ω into C. If f maps e...

Using the S.Lie’s infinitesimal approach we establish the connection between integrability of a one-parameter family of the Riccati equations and the stationary KdV hierarchy. In this paper we will suggest a method for integrating a one-parameter family of the Riccati equations ux + u 2 = f(x, λ) (1) based on their Lie symmetries. Here f(x, λ) = λ + λVn−1(x) + · · ·+ λV1(x) + V0(x) and λ is an ...