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.

A Quantum Gauge Group Approach to the 2D SU(n) WZNW Model

The canonical quantization of the WZNW model provides a complete set of exchange relations in the enlarged chiral state spaces that include the Gauss components of the monodromy matrices. Regarded as new dynamical variables, the elements of the latter cannot be identified -- they satisfy different exchange relations. Accordingly, the two dimensional theory expressed in terms of the left and right movers' fields does not automatically respect monodromy invariance. Continuing our recent analysis of the problem by gauge theory methods we conclude that physical states (on which the two dimensional field acts as a single valued operator) are invariant under the (permuted) coproduct of the left and right $U_q(sl(n))$. They satisfy additional constraints fully described for n=2.Comment: 10 pages, LATEX (Proposition 4.2 corrected, one reference added

Operator realization of the SU(2) WZNW model

Decoupling the chiral dynamics in the canonical approach to the WZNW model requires an extended phase space that includes left and right monodromy variables. Earlier work on the subject, which traced back the quantum qroup symmetry of the model to the Lie-Poisson symmetry of the chiral symplectic form, left some open questions: - How to reconcile the monodromy invariance of the local 2D group valued field (i.e., equality of the left and right monodromies) with the fact that the latter obey different exchange relations? - What is the status of the quantum group symmetry in the 2D theory in which the chiral fields commute? - Is there a consistent operator formalism in the chiral and in the extended 2D theory in the continuum limit? We propose a constructive affirmative answer to these questions for G=SU(2) by presenting the chiral quantum fields as sums of chiral vertex operators and q-Bose creation and annihilation operators.Comment: 18 pages, LATE

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

Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model

The zero modes' Fock space for the extended chiral $su(2)$ WZNW model gives room to a realization of the Grothendieck fusion ring of representations of the restricted $U_q sl(2)$ quantum universal enveloping algebra (QUEA) at an even ($2h$-th) root of unity, and of its extension by the Lusztig operators. It is shown that expressing the Drinfeld images of canonical characters in terms of Chebyshev polynomials of the Casimir invariant $C$ allows a streamlined derivation of the characteristic equation of $C$ from the defining relations of the restricted QUEA. The properties of the fusion ring of the Lusztig's extension of the QUEA in the zero modes' Fock space are related to the braiding properties of correlation functions of primary fields of the extended $su(2)_{h-2}$ current algebra model.Comment: 36 pages, 1 figure; version 3 - improvements in Sec. 2 and 3: definitions of the double, as well as R- (and M-)matrix changed to fit the zero modes' one

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.

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