Metrics with Galilean Conformal Isometry

The Galilean Conformal Algebra (GCA) arises in taking the non-relativistic limit of the symmetries of a relativistic Conformal Field Theory in any dimensions. It is known to be infinite-dimensional in all spacetime dimensions. In particular, the 2d GCA emerges out of a scaling limit of linear combinations of two copies of the Virasoro algebra. In this paper, we find metrics in dimensions greater than two which realize the finite 2d GCA (the global part of the infinite algebra) as their isometry by systematically looking at a construction in terms of cosets of this finite algebra. We list all possible sub-algebras consistent with some physical considerations motivated by earlier work in this direction and construct all possible higher dimensional non-degenerate metrics. We briefly study the properties of the metrics obtained. In the standard one higher dimensional "holographic" setting, we find that the only non-degenerate metric is Minkowskian. In four and five dimensions, we find families of non-trivial metrics with a rather exotic signature. A curious feature of these metrics is that all but one of them are Ricci-scalar flat.Comment: 20 page

Influence of the Pressure on the Product Distribution in the Oxidative Dehydrogenation of Propane over a Ga2O3/MoO3 Catalyst

The yields and selectivities in both the catalyzed and non-catalyzed oxidative dehydrogenation of propane were found to increase with increasing pressure. The results showed that the maximum yields of valuable ODH products could be obtained by adjusting only reactants' partial pressure, while keeping their ratio constant

Lowest Weight Representations of Super Schrodinger Algebras in One Dimensional Space

Lowest weight modules, in particular, Verma modules over the N = 1,2 super Schrodinger algebras in (1+1) dimensional spacetime are investigated. The reducibility of the Verma modules is analyzed via explicitly constructed singular vectors. The classification of the irreducible lowest weight modules is given for both massive and massless representations. A vector field realization of the N = 1, 2 super Schrodinger algebras is also presented.Comment: 19 pages, no figur

Gravity duals for non-relativistic CFTs

We attempt to generalize the AdS/CFT correspondence to non-relativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and compute some two-point correlators. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions.Comment: 12 pages; v2, v3, v4: added references, minor corrections; v3: cleaned up and generalized dust; v4: closer to published versio

Fluiddynamik des Kammerwassers beim chronischen einfachen Glaukom: Mechanismen der Drucknormalisierung durch ein künstliches Abflusssystem

Zusammenfassung: Die Wechselwirkung zwischen Kräften, Verteilung und Absorption des Kammerwassers im subkonjunktivalen Gewebe wird anhand eines kürzlich publizierten theoretischen Modells untersucht, das die Produktion von Flüssigkeit im Auge und deren Eliminierung durch das Trabekelwerk, das uveosklerale Gewebe und einen Shunt beschreibt. Zielgröße dabei ist der intraokulare Druck. Die Mechanismen von neu geschaffenen Abflusswegen werden mithilfe der Theorie der porösen Medien dargestellt, die sich auf ein Sickerkissen beziehen, das unter dem subkonjunktivalen Gewebe liegt. Die rechnerische Analyse basiert auf der Geometrie und den Parametern, die das Zu- und Abflusssystem charakterisieren. Diese sind durch die Produktion von Kammerwasser, den chirurgisch angelegten Abflusskanal, sodann durch die Resorption in den episkleralen Gefäßen und durch die hydraulischen Eigenschaften des subkonjunktivalen Gewebes und des Sickerkissens sowie durch dessen Geometrie gegeben. Anhand parametrischer Untersuchungen können klinische Befunde physikalisch begründet werde

SO(2,1) conformal anomaly: Beyond contact interactions

The existence of anomalous symmetry-breaking solutions of the SO(2,1) commutator algebra is explicitly extended beyond the case of scale-invariant contact interactions. In particular, the failure of the conservation laws of the dilation and special conformal charges is displayed for the two-dimensional inverse square potential. As a consequence, this anomaly appears to be a generic feature of conformal quantum mechanics and not merely an artifact of contact interactions. Moreover, a renormalization procedure traces the emergence of this conformal anomaly to the ultraviolet sector of the theory, within which lies the apparent singularity.Comment: 11 pages. A few typos corrected in the final versio