Two-dimensional Maxwell-dilaton quantum gravity on AdS2 with radius l and a constant electric field E is studied. In conformal gauge, this is equivalent to a CFT on a strip. In order to maintain consistent boundary conditions, the usual conformal diffeomorphisms must be accompanied by a certain U(1) gauge transformation. The resulting conformal transformations are generated by a twisted stress ...

Abstract The application of transformation optics to the development intriguing electromagnetic devices can produce weakly anisotropic or isotropic media with assistance quasi-conformal and/or conformal mapping, as opposed strongly produced by general mappings; however, it is typically limited two-dimensional applications. By addressing mapping between two manifolds embedded in three-dimensiona...

The AdS/CFT transformation relates two nonlinear realizations of (super)conformal groups: their realization in the appropriate field theories in Minkowski space with a Goldstone dilaton field and their realization as (super)isometry groups of AdS (super)spaces. It exists already at the classical level and maps the field variables and space-time coordinates of the given (super)conformal field th...

We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala’s conjecture that the Hausdorff dimension of a k-quasicircle is at most 1 + k. A homeomorphism φ of planar domains is called k-quasiconformal, if it belongs locally to the Sobolev class W 1 2 and its ...

We present a transformation optics approach for molding the light flow at the deep-subwavelength scale, using metamaterials with uniquely designed dispersion. By conformal transformation of the electromagnetic space, we develop a methodology for realizing subwavelength ray optics with curved ray trajectories. This enables deep-subwavelength-scale beams to flow through two- or three-dimensional ...

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 Fra...

In the Randall-Sundrum scenario we analyze the dynamics of a spherically symmetric 3-brane when the bulk is filled with matter fields. Considering a global conformal transformation whose factor is the Z2 symmetric warp we find a new set of exact dynamical solutions for which gravity is bound to the brane. The set corresponds to a certain class of conformal bulk fields. We discuss the geometries...

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...