Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model

We define the chiral zero modes' phase space of the G=SU(n) Wess-Zumino-Novikov-Witten model as an (n-1)(n+2)-dimensional manifold M_q equipped with a symplectic form involving a special 2-form - the Wess-Zumino (WZ) term - which depends on the monodromy M. This classical system exhibits a Poisson-Lie symmetry that evolves upon quantization into an U_q(sl_n) symmetry for q a primitive even root of 1. For each constant solution of the classical Yang-Baxter equation we write down explicitly a corresponding WZ term and invert the symplectic form thus computing the Poisson bivector of the system. The resulting Poisson brackets appear as the classical counterpart of the exchange relations of the quantum matrix algebra studied previously. We argue that it is advantageous to equate the determinant D of the zero modes' matrix to a pseudoinvariant under permutations q-polynomial in the SU(n) weights, rather than to adopt the familiar convention D=1.Comment: 30 pages, LaTeX, uses amsfonts; v.2 - small corrections, Appendix and a reference added; v.3 - amended version for J. Phys.

Indecomposable U_q(sl_n) modules for q^h = -1 and BRS intertwiners

A class of indecomposable representations of U_q(sl_n) is considered for q an even root of unity (q^h = -1) exhibiting a similar structure as (height h) indecomposable lowest weight Kac-Moody modules associated with a chiral conformal field theory. In particular, U_q(sl_n) counterparts of the Bernard-Felder BRS operators are constructed for n=2,3. For n=2 a pair of dual d_2(h) = h dimensional U_q(sl_2) modules gives rise to a 2h-dimensional indecomposable representation including those studied earlier in the context of tensor product expansions of irreducible representations. For n=3 the interplay between the Poincare'-Birkhoff-Witt and (Lusztig) canonical bases is exploited in the study of d_3(h) = h(h+1)(2h+1)/6 dimensional indecomposable modules and of the corresponding intertwiners

Chiral zero modes of the SU(n) WZNW model

We define the chiral zero modes' phase space of the G=SU(n) Wess-Zumino-Novikov-Witten (WZNW) model as an (n-1)(n+2)-dimensional manifold M_q equipped with a symplectic form involving a special 2-form - the Wess-Zumino (WZ) term - which depends on the monodromy M. This classical system exhibits a Poisson-Lie symmetry that evolves upon quantization into an U_q(sl_n) symmetry for q a primitive even root of 1. For each constant solution of the classical Yang-Baxter equation (CYBE) we write down explicitly a corresponding WZ term and invert the symplectic form thus computing the Poisson bivector of the system. The resulting Poisson brackets appear as the classical counterpart of the exchange relations of the quantum matrix algebra studied previously. We argue that it is advantageous to equate the determinant D of the zero modes' matrix to a pseudoinvariant under permutations polynomial in the SU(n) weights, rather than to adopt the familiar convention D=1

Quantization of U_q[so(2n+1)] with deformed para-Fermi operators

The observation that n pairs of para-Fermi (pF) operators generate the universal enveloping algebra of the orthogonal Lie algebra so(2n+1) is used in order to define deformed pF operators. It is shown that these operators are an alternative to the Chevalley generators. On this background Uq[so(2n+1)] and its "Cartan-Weyl" generators are written down entirely in terms of deformed pB operators.Comment: plain TeX, Preprint INRNE-TH-93/7, 6

Quantum matrix algebra for the SU(n) WZNW model

The zero modes of the chiral SU(n) WZNW model give rise to an intertwining quantum matrix algebra A generated by an n x n matrix a=(a^i_\alpha) (with noncommuting entries) and by rational functions of n commuting elements q^{p_i}. We study a generalization of the Fock space (F) representation of A for generic q (q not a root of unity) and demonstrate that it gives rise to a model of the quantum universal enveloping algebra U_q(sl_n), each irreducible representation entering F with multiplicity 1. For an integer level k the complex parameter q is an even root of unity, q^h=-1 (h=k+n) and the algebra A has an ideal I_h such that the factor algebra A_h = A/I_h is finite dimensional.Comment: 48 pages, LaTeX, uses amsfonts; final version to appear in J. Phys.

Extended chiral algebras in the SU(2)_0 WZNW model

We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU(2)_0 WZNW model. These have a form almost identical to that found in the c=-2 model but have, in addition, an extended Kac-Moody structure. Moreover on Hamiltonian reduction these SU(2)_0 W-algebras exactly reduce to those found in c=-2. We explicitly find the free field representations for the chiral j=2 and j=3 operators which have respectively a fermionic doublet and bosonic triplet nature. The correlation functions of these operators accounts for the rational solutions of the Knizhnik-Zamolodchikov equation that we find. We explicitly compute the full algebra of the j=2 operators and find that the associativity of the algebra is only guaranteed if certain null vectors decouple from the theory. We conjecture that these algebras may produce a quasi-rational conformal field theory.Comment: 18 pages LATEX. Minor corrections. Full j=2 algebra adde

Adsorption and reaction of CO on (Pd–)Al2O3 and (Pd–)ZrO2: vibrational spectroscopy of carbonate formation

γ-Alumina is widely used as an oxide support in catalysis, and palladium nanoparticles supported by alumina represent one of the most frequently used dispersed metals. The surface sites of the catalysts are often probed via FTIR spectroscopy upon CO adsorption, which may result in the formation of surface carbonate species. We have examined this process in detail utilizing FTIR to monitor carbonate formation on γ-alumina and zirconia upon exposure to isotopically labelled and unlabelled CO and CO2. The same was carried out for well-defined Pd nanoparticles supported on Al2O3 or ZrO2. A water gas shift reaction of CO with surface hydroxyls was detected, which requires surface defect sites and adjacent OH groups. Furthermore, we have studied the effect of Cl synthesis residues, leading to strongly reduced carbonate formation and changes in the OH region (isolated OH groups were partly replaced or were even absent). To corroborate this finding, samples were deliberately poisoned with Cl to an extent comparable to that of synthesis residues, as confirmed by Auger electron spectroscopy. For catalysts prepared from Cl-containing precursors a new CO band at 2164 cm−1 was observed in the carbonyl region, which was ascribed to Pd interacting with Cl. Finally, the FTIR measurements were complemented by quantification of the amount of carbonates formed via chemisorption, which provides a tool to determine the concentration of reactive defect sites on the alumina surface

Indecomposable U_q(sl_n) modules for q^h = -1 and BRS intertwiners

A class of indecomposable representations of U_q(sl_n) is considered for q an even root of unity (q^h = -1) exhibiting a similar structure as (height h) indecomposable lowest weight Kac-Moody modules associated with a chiral conformal field theory. In particular, U_q(sl_n) counterparts of the Bernard-Felder BRS operators are constructed for n=2,3. For n=2 a pair of dual d_2(h) = h dimensional U_q(sl_2) modules gives rise to a 2h-dimensional indecomposable representation including those studied earlier in the context of tensor product expansions of irreducible representations. For n=3 the interplay between the Poincare'-Birkhoff-Witt and (Lusztig) canonical bases is exploited in the study of d_3(h) = h(h+1)(2h+1)/6 dimensional indecomposable modules and of the corresponding intertwiners.Comment: 31 pages, LaTeX, amsfonts, amssym

Modulator-controlled synthesis of microporous STA-26, an interpenetrated 8,3-connected zirconium MOF with the the-i topology, and its reversible lattice shift

The authors acknowledge the support of the EPSRC/St Andrews Criticat CDT (RRRP, PAW) and the European Community Seventh Framework Program (FP7/2007-2013) number 608490 (project M4CO2) (KKC, MYM, KIH, PAW). SEA would like to thank the Royal Society and Wolfson Foundation for a merit award. This research made use of the Balena High Performance Computing (HPC) Service at the University of Bath. The research data (and/or materials) supporting this publication can be accessed at DOI: http://dx.doi.org/10.17630/6ffeed8a-e75f-4648-968f-3ed32a94e9a0.A fully interpenetrated 8,3-connected zirconium MOF with the the-i topology type, STA-26 (St Andrews porous material-26), has been prepared using the 4,4',4"-(2,4,6-trimethylbenzene-1,3,5-triyl)tribenzoate (TMTB) tritopic linker with formic acid as a modulating agent. In the as-prepared form STA-26 possesses Im-3m symmetry compared with the Pm-3m symmetry of the non-interpenetrated analogue, NU-1200, prepared using benzoic acid as a modulator. Upon removal of residual solvent there is a shift between the interpenetrating lattices and a resultant symmetry change to Cmcm which is fully reversible. This is observed by X-ray diffraction and 13C MAS NMR is also found to be remarkably sensitive to the structural transition. Furthermore, heating STA-26(Zr) in vacuum dehydroxylates the Zr6 nodes leaving coordinatively unsaturated Zr4+ sites, as shown by IR spectroscopy using CO and CD3CN as probe molecules. Nitrogen adsorption at 77 K together with grand canonical Monte Carlo simulations confirms a microporous, fully interpenetrated, structure with pore volume 0.53 cm3 g−1 while CO2 adsorption at 196 K reaches 300 cm3 STP g−1 at 1 bar. While the pore volume is smaller than that of its non-interpenetrated mesoporous analogue, interpenetration makes the structure more stable to moisture adsorption and introduces shape selectivity in adsorption.PostprintPeer reviewe