Null scrolls as fluctuating surfaces: a new simple way to construct extrinsic string solutions

We exhibit a surprising phenomenon that happens in the conformal Lorentz Minkowski three space, which has no counterpart in a Riemannian setting. Whenever a curve, no matter its causal character, propagates transversely through a conformal geodesic null vector field, it is generating the worldsheet of an extrinsic Polyakov string solution. Furthermore, the Polyakov extrinsic energy of these solutions only depend on the worldsheet topology and it can be computed not only intrinsically, but also holographically by measuring the hyperbolic angles in the boundary corners. This geometric approach, to provide extrinsic string solutions, can be considered as an alternative to the Pohlmeyer reduced mechanism. Then, we describe how to translate these solutions to the language of Pohlmeyer theory. We will also show that any curve in the conformal boundary of the anti de Sitter 3-space can be viewed as a piece of the generalized Wilson loops associated with an extrinsic string solution obtained by this geometric mechanism.