W-algebras and superalgebras from constrained WZW models: A group theoretical classification

We present a classification ofW algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with anSl(2) subalgebra (resp.OSp(1/2) superalgebra) of a simple Lie algebra (resp. superalgebra)G. However, the determination of anU(1) _Y factor, commuting withSl(2) (resp.OSp(1/2)), appears, when it exists, particularly useful to characterize the correspondingW algebra. The (super) conformal spin contents of eachW (super) algebra is performed. The class of all the superconformal algebras (i.e. with conformal spinss<=2) is easily obtained as a byproduct of our general results.     

Extended super-Kač-Moody algebras and their super-derivation algebras

We study theN-extended super-Ka-Moody algebras, i.e. extensions of the Lie algebra of the loop group over the super-circleA _N . The extensions are characterized by 2-cocycles which are computed in terms of the cyclic cohomology of the Grassmann algebra withN generators. The graded algebra of super-derivations compatible with each extension is determined. The casesN=1,2,3 are examined in detail and their relation with the Ademollo et al. superconformal algebras is discussed. We examine the possibility of defining new superconformal algebras which, forN>1, generalize theN=1 Ramond-Neveu-Schwarz algebra.     

Unsymmetrically substituted furoxans. Part 16 . Reaction of benzenesulfonyl substituted furoxans with ethanol and ethanethiol in basic medium

The use of benzenesulfonyl substituted furoxans as flexible intermediates for the synthesis of new functionalized furoxans interesting for their potential biological properties is discussed. Reaction of benzenesul-fonylphenylsulfonylfuroxan isomers 7a and 7b with ethanol and ethanethiol in basic medium affords the expected ethers and sulphides respectively. Reaction of bis(benzenesulfonyl)furoxan ( 1 ) with ethanol in basic medium gives 3-benzenesulfonyl-4-ethoxyfuroxan ( 2 ) or diethoxyfuroxan (3), according to the experimental procedure. In contrast the reaction of 1 with ethanethiol gives a mixture of substitution compounds and the 4-benzenesulfonyl-3-ethylthiofurazan ( 11 ). The structure of the compounds has been assigned by nmr spectroscopy and, in the case of 3-benzenesulfonyl-4-ethylthiofuroxan ( 9b ), confirmed by X-ray analysis.     

Quantum Groups and the Genetic Code

The quantum algebra in the limit q 0 is proposed as a symmetry algebra for the genetic code. The nucleotide triplets (codons) in the DNA chain are classified in crystal bases. This construction can be compared to the baryon classification from quarks in particle physics, one main difference being the natural order in the state constituents provided by the crystal base. An operator ensuring the correspondence between codons and amino acids is constructed from the above algebra: two codons corresponding to the same or different amino acids acquire the same or different eigenvalues respectively. Then a set of relations between the physicochemical properties of the amino acids are derived and compared with the experimental data. Correlations of the codon usage for quartets and sextets are determined, fitting naturally in the framework of this model.     

on submicron rings and their application for coherent nanoelectronic devices

Electron-phase modulation in magnetic and electric fields will be presented in In_0.75Ga_0.25As Aharonov–Bohm (AB) rings. The zero Schottky barrier of this material made it possible to nanofabricate devices with radii down to below 200 nm without carrier depletion. We shall present a fabrication scheme based on wet and dry etching that yielded excellent reproducibility, very high contrast of the oscillations and good electrical gating. The operation of these structures is compatible with closed-cycle refrigeration and suggests that this process can yield coherent electronic circuits that do not require cryogenic liquids. The InGaAs/AlInAs heterostructure was grown by MBE on a GaAs substrate [F. Capotondi, G. Biasiol, D. Ercolani, V. Grillo, E. Carlino, F. Romanato, L. Sorba, Thin Solid Films 484 (2005) 400], and in light of the large effective g-factor and the absence of the Schottky barrier is a material system of interest for the investigation of spin-related effects [W. Desrat, F. Giazotto, V. Pellegrini, F. Beltram, F. Capotondi, G. Biasiol, L. Sorba, D.K. Maude, Phys. Rev. B 69 (2004) 245324; W. Desrat, F. Giazotto, V. Pellegrini, M. Governale, F. Beltram, F. Capotondi, G. Biasiol, L. Sorba, Phys. Rev. B 71 (2005) 153314; J. Nitta, T. Akazaki, H. Takayanagi, T. Enoki, Phys. Rev. Lett. 78 (1997) 1335] and the realization of hybrid superconductor/semiconductor devices [Th. Schäpers, A. Kaluza, K. Neurohr, J. Malindretos, G. Crecelius, A. van der Hart, H. Hardtdegen, H. Lüth, Appl. Phys. Lett. 71 (1997) 3575].     

Strings fromN=2 gauged Wess-Zumino-Witten models

We present an algebraic approach to string theory. An embedding ofsl(2|1) in a super Lie algebra together with a grading on the Lie algebra determines a nilpotent subalgebra of the super Lie algebra. Chirally gauging this subalgebra in the corresponding Wess-Zumino-Witten model, breaks the affine symmetry of the Wess-Zumino-Witten model to some extension of theN=2 superconformal algebra. The extension is completely determined by thesl(2|1) embedding. The realization of the superconformal algebra is determined by the grading. For a particular choice of grading, one obtains in this way, after twisting, the BRST structure of a string theory. We classify all embeddings ofsl(2|1) into Lie super algebras and give a detailed account of the branching of the adjoint representation. This provides an exhaustive classification and characterization of both all extendedN=2 superconformal algebras and all string theories which can be obtained in this way.     

On embeddings of gauge groups in Yang-Mills theory

We discuss some group theoretical properties of Yang-Mills theories. We consider conditions necessary and sufficient to decide if the gauge field is reducible and prove some related theorems. We give criteria for embeddings and work out the case of SU (3) explicitly.