Towards a world‐sheet description of doubled geometry in string theory

Starting from a sigma‐model for a doubled target‐space geometry, we show that the number of target‐space dimensions can be reduced by half through a gauging procedure. We apply this formalism to a class of backgrounds relevant for double field theory, and illustrate how choosing different gaugings leads to string‐theory configurations T‐dual to each other. We furthermore discuss that given a conformal doubled theory, the reduced theories are conformal as well. As an example we consider the three‐dimensional WZW model and show that the only possible reduced backgrounds are the cigar and trumpet CFTs in two dimensions, which are indeed T‐dual to each other.     

Molecular Structure of Phosphinidene Phosphates

Abstract

Alkalimetal diphenylphosphinites degrade (Ph-P)₅ and P₄ to give anions containing a chain of 2, 3 or 4 four- and two-coordinated phosphorus atoms. Representatives of the chain with two four-coordinated and one two-coordinated P atoms became first available from the aminolysis of tris (phosphoryl)phosphides¹.     

Synthesis,Redox Behavior,Sensitizer Activity,and Oxygen Transfer of Covalently Bound Polymeric Porphyrins

Metal complexes of covalently bound porphyrins are used as sensitive probes for several investigations. Substituted derivatives of tetraphenyl-porphin, phthalocyanine, and naphthalocyanine are synthesized at positively and negatively charged as well as uncharged polymers. The photo-redox activities were studied under irradiation with visible light in the presence of a donor and an acceptor. The triplet life times of covalently bound porphyrin moieties are strongly enhanced compared with the analogous monomeric porphyrins. In addition, the polymer binding results in higher photocatalytic activity. The electron-transfer reactions of Mn(III)-containing porphyrins using the reducing agent dithionite are strongly influenced by the polymer environment. In contrast to monomeric Mn(III)-porphyrins, the porphyrins containing polymers exhibit a two-step reduction which may be due to the change of the conformation of the polymer coil. The catalytic epoxidation of 2,5-dihydrofuran with hypochlorite with formation of 3,4-epoxytetrahydrofuran occurs with water-soluble porphyrins in water. No influence of the polymer environment exists. The different reactions require reaction times from milliseconds up to hours.