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.

Reply

No Abstract.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50352/1/410320425_ftp.pd

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

Production of docosahexaenoic acid by Aurantiochytrium sp. ATCC PRA-276

The high costs and environmental concerns associated with using marine resources as sources of oils rich in polyunsaturated fatty acids have prompted searches for alternative sources of such oils. Some microorganisms, among them members of the genus Aurantiochytrium, can synthesize large amounts of these biocompounds. However, various parameters that affect the polyunsaturated fatty acids production of these organisms, such as the carbon and nitrogen sources supplied during their cultivation, require further elucidation. The objective of this investigation was to study the effect of different concentrations of carbon and total nitrogen on the production of polyunsaturated fatty acids, particularly docosahexaenoic acid, by Aurantiochytrium sp. ATCC PRA-276. We performed batch system experiments using an initial glucose concentration of 30 g/L and three different concentrations of total nitrogen, including 3.0, 0.44, and 0.22 g/L, and fed-batch system experiments in which 0.14 g/L of glucose and 0.0014 g/L of total nitrogen were supplied hourly. To assess the effects of these different treatments, we determined the biomass, glucose, total nitrogen and polyunsaturated fatty acids concentration. The maximum cell concentration (23.9 g/L) was obtained after 96 h of cultivation in the batch system using initial concentrations of 0.22 g/L total nitrogen and 30 g/L glucose. Under these conditions, we observed the highest level of polyunsaturated fatty acids production (3.6 g/L), with docosahexaenoic acid and docosapentaenoic acid ω6 concentrations reaching 2.54 and 0.80 g/L, respectively

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

Near-Infrared, Adaptive Optics Observations of the T Tauri Multiple-Star System

With high-angular-resolution, near-infrared observations of the young stellar object T Tauri at the end of 2002, we show that, contrary to previous reports, none of the three infrared components of T Tau coincide with the compact radio source that has apparently been ejected recently from the system (Loinard, Rodriguez, and Rodriguez 2003). The compact radio source and one of the three infrared objects, T Tau Sb, have distinct paths that depart from orbital or uniform motion between 1997 and 2000, perhaps indicating that their interaction led to the ejection of the radio source. The path that T Tau Sb took between 1997 and 2003 may indicate that this star is still bound to the presumably more massive southern component, T Tau Sa. The radio source is absent from our near-infrared images and must therefore be fainter than K = 10.2 (if located within 100 mas of T Tau Sb, as the radio data would imply), still consistent with an identity as a low-mass star or substellar object.Comment: 11 pages, 3 figures, submitted to ApJ

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.

A Spitzer IRS Survey of NGC 1333: Insights into disk evolution from a very young cluster

We report on the {\lambda} = 5-36{\mu}m Spitzer Infrared Spectrograph spectra of 79 young stellar objects in the very young nearby cluster NGC 1333. NGC 1333's youth enables the study of early protoplanetary disk properties, such as the degree of settling as well as the formation of gaps and clearings. We construct spectral energy distributions (SEDs) using our IRS data as well as published photometry and classify our sample into SED classes. Using "extinction-free" spectral indices, we determine whether the disk, envelope, or photosphere dominates the spectrum. We analyze the dereddened spectra of objects which show disk dominated emission using spectral indices and properties of silicate features in order to study the vertical and radial structure of protoplanetary disks in NGC 1333. At least nine objects in our sample of NGC 1333 show signs of large (several AU) radial gaps or clearings in their inner disk. Disks with radial gaps in NGC 1333 show more-nearly pristine silicate dust than their radially continuous counterparts. We compare properties of disks in NGC 1333 to those in three other well studied regions, Taurus-Auriga, Ophiuchus and Chamaeleon I, and find no difference in their degree of sedimentation and dust processing.Comment: 67 pages, 20 figures, accepted to The Astrophysical Journal Supplement Serie

Probing stellar accretion with mid-infrared hydrogen lines

In this paper we investigate the origin of the mid-infrared (IR) hydrogen recombination lines for a sample of 114 disks in different evolutionary stages (full, transitional and debris disks) collected from the {\it Spitzer} archive. We focus on the two brighter {H~{\sc i}} lines observed in the {\it Spitzer} spectra, the {H~{\sc i}}(7-6) at 12.37$\mu$m and the {H~{\sc i}}(9-7) at 11.32$\mu$m. We detect the {H~{\sc i}}(7-6) line in 46 objects, and the {H~{\sc i}}(9-7) in 11. We compare these lines with the other most common gas line detected in {\it Spitzer} spectra, the {[Ne~{\sc iii}]} at 12.81$\mu$m. We argue that it is unlikely that the {H~{\sc i}} emission originates from the photoevaporating upper surface layers of the disk, as has been found for the {[Ne~{\sc iii}]} lines toward low-accreting stars. Using the {H~{\sc i}}(9-7)/{H~{\sc i}}(7-6) line ratios we find these gas lines are likely probing gas with hydrogen column densities of 10$^{10}$-10$^{11}$~cm$^{-3}$. The subsample of objects surrounded by full and transitional disks show a positive correlation between the accretion luminosity and the {H~{\sc i}} line luminosity. These two results suggest that the observed mid-IR {H~{\sc i}} lines trace gas accreting onto the star in the same way as other hydrogen recombination lines at shorter wavelengths. A pure chromospheric origin of these lines can be excluded for the vast majority of full and transitional disks.We report for the first time the detection of the {H~{\sc i}}(7-6) line in eight young (< 20~Myr) debris disks. A pure chromospheric origin cannot be ruled out in these objects. If the {H~{\sc i}}(7-6) line traces accretion in these older systems, as in the case of full and transitional disks, the strength of the emission implies accretion rates lower than 10$^{-10}$M$_{\odot}$/yr. We discuss some advantages of extending accretion indicators to longer wavelengths

Emission from Water Vapor and Absorption from Other Gases at 5-7.5 Microns in Spitzer-IRS Spectra of Protoplanetary Disks

We present spectra of 13 T Tauri stars in the Taurus-Auriga star-forming region showing emission in Spitzer Space Telescope Infrared Spectrograph (IRS) 5-7.5 micron spectra from water vapor and absorption from other gases in these stars' protoplanetary disks. Seven stars' spectra show an emission feature at 6.6 microns due to the nu_2 = 1-0 bending mode of water vapor, with the shape of the spectrum suggesting water vapor temperatures > 500 K, though some of these spectra also show indications of an absorption band, likely from another molecule. This water vapor emission contrasts with the absorption from warm water vapor seen in the spectrum of the FU Orionis star V1057 Cyg. The other six of the thirteen stars have spectra showing a strong absorption band, peaking in strength at 5.6-5.7 microns, which for some is consistent with gaseous formaldehyde (H2CO) and for others is consistent with gaseous formic acid (HCOOH). There are indications that some of these six stars may also have weak water vapor emission. Modeling of these stars' spectra suggests these gases are present in the inner few AU of their host disks, consistent with recent studies of infrared spectra showing gas in protoplanetary disks.Comment: 33 pages, 9 figures, to appear in the 20 August, 2014, V791 - 2 issue of the Astrophysical Journa