Recently an alternative description of 2d supergravities in terms of graded Poisson-Sigma models (gPSM) has been given. As pointed out previously by the present authors a certain subset of gPSMs can be interpreted as "genuine" supergravity, fulfilling the well-known limits of supergravity, albeit deformed by the dilaton field. In our present paper we show that precisely that class of gPSMs corresponds one-to-one to the known dilaton supergravity superfield theories presented a long time ago by Park and Strominger. Therefore, the unique advantages of the gPSM approach can be exploited for the latter: We are able to provide the first complete classical solution for any such theory. On the other hand, the straightforward superfield formulation of the point particle in a supergravity background can be translated back into the gPSM frame, where "supergeodesics" can be discussed in terms of a minimal set of supergravity field degrees of freedom. Further possible applications like the (almost) trivial quantization are mentioned.

In this paper various extensions of the design strategy of transformation media are proposed. We show that it is possible to assign different transformed spaces to the field strength tensor (electric field and magnetic induction) and to the excitation tensor (displacement field and magnetic field), resp. In this way, several limitations of standard transformation media can be overcome. In particular it is possible to provide a geometric interpretation of non-reciprocal as well as indefinite materials. We show that these transformations can be complemented by a continuous version of electric-magnetic duality and comment on the relation to the complementary approach of field-transforming metamaterials.Comment: 11 pages, 3 figures, v2: typos, new figures, REVTeX, v3: typos, new example added, final versio

Fermionic extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In addition, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to algebras which can be interpreted as supergravities in the usual sense (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of the dilaton field. With very straightforward and natural assumptions on them -like demanding rigid supersymmetry in a certain flat limit, or linking the anti-commutator of certain fermionic charges to the Hamiltonian constraint-in the "genuine" supergravity obtained in this way the ambiguities disappear, as well as the obstructions referred to above. Thus all especially interesting bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.) under these conditions possess a unique fermionic extension and are free from new singularities. The superspace supergravity model of Howe is found as a special case of this supergravity action. For this class of models the relation between bosonic potential and prepotential does not introduce obstructions as well.

We present a systematic discussion of supersymmetric solutions of 2D dilaton supergravity. In particular those solutions which retain at least half of the supersymmetries are ground states with respect to the bosonic Casimir function (essentially the ADM mass). Nevertheless, by tuning the prepotential appropriately, black hole solutions may emerge with an arbitrary number of Killing horizons. The absence of dilatino and gravitino hair is proven. Moreover, the impossibility of supersymmetric dS ground states and of nonextremal black holes is confirmed, even in the presence of a dilaton. In these derivations the knowledge of the general analytic solution of 2D dilaton supergravity plays an important rôle. The latter result is addressed in the more general context of gPSMs which have no supergravity interpretation.Finally it is demonstrated that the inclusion of non-minimally coupled matter, a step which is already nontrivial by itself, does not change these features in an essential way. * 4 Conventions and light cone coordinates are summarized in app. A. 5 CDV solutions with u = 0 must obey u ′ /u = − 1 2 Z, which leads to C S = 0 while C B = 0. Clearly, they cannot respect both supersymmetries.

Based on a recent work by Schuller et al., a geometric representation of all skewonless, nonbirefringent linear media is obtained. The derived constitutive law is based on a "core", encoding the optical metric up to a constant. All further corrections are provided by two (anti-)selfdual bivectors, and an "axion". The bivectors are found to vanish if the optical metric has signature (3,1) -that is, if the Fresnel equation is hyperbolic. We propose applications of this result in the context of transformation optics and premetric electrodynamics.