Local Duality Research Articles

Finite-dimensional duality on the generalized Lie algebra 𝔰𝔩(2)q

We show a local duality between the left and right finite-dimensional representations on the enveloping algebra of (2)q, the generalized Lie algebra introduced by Lyubashenko and Sudbery. This duality works in a general context of algebras satisfying certain algebraic properties; our goal in this paper is to prove that the enveloping algebra of (2)q satisfies these abstract properties.

Inverse Relations and Schauder Bases

The concept of inter-changes of Schauder bases is used to interpret inverse relations for sequences. For a given power series, the interplay between different representations by Schauder bases can result in combinatorial identities, new or known. Local cohomology residues and local duality are used for computations. The viewpoint of Riordan arrays is examined using Schauder bases.

Quark–hadron duality: resonances and the onset of scaling

We examine the origin of Bloom-Gilman duality and the relationship between resonances and scaling in deep-inelastic scattering. A simple quantum mechanical model is used to illustrate the essential features of Bloom-Gilman duality at low momentum transfer. As an application of local duality, we discuss model-independent relations between structure functions at x ~ 1 and elastic electromagnetic form factors.

Testing an approximation to large-Nc QCD with a toy model

We consider a simple model of large-Nc QCD defined by a spectrum consisting of an infinite set of equally spaced zero-width vector resonances. This model is an excellent theoretical laboratory for investigating certain approximation schemes which have been used recently in calculations of hadronic parameters, such as the Minimal Hadronic Approximation. We also comment on some of the questions concerning issues of local duality versus global duality and finite-energy sum rules.

Leading and higher twists in the proton polarized structure functiong1pat large Bjorkenx

A phenomenological parametrization of the proton polarized structure function ${g}_{1}^{p}{(x,Q}^{2})$ is developed for $x\ensuremath{\gtrsim}0.02$ using deep inelastic data up to $\ensuremath{\sim}50 (\mathrm{GeV}{/c)}^{2}$ as well as available experimental results on both photo- and electroproduction of proton resonances. According to the new parametrization the generalized Drell-Hearn-Gerasimov sum rule is predicted to have a zero-crossing point at ${Q}^{2}=0.16\ifmmode\pm\else\textpm\fi{}0.04 (\mathrm{GeV}{/c)}^{2}.$ Then, low-order polarized Nachtmann moments are estimated and their ${Q}^{2}$ behavior is investigated in terms of leading and higher twists for ${Q}^{2}\ensuremath{\gtrsim}1 (\mathrm{GeV}{/c)}^{2}.$ The leading twist is treated at NLO in the strong coupling constant and the effects of higher orders of the perturbative series are estimated using soft-gluon resummation techniques. In the case of the first moment, higher-twist effects are found to be quite small for ${Q}^{2}\ensuremath{\gtrsim}1 (\mathrm{GeV}{/c)}^{2},$ and the singlet axial charge has been determined to be ${a}_{0}[10 (\mathrm{GeV}{/c)}^{2}]=0.16\ifmmode\pm\else\textpm\fi{}0.09.$ In the case of higher order moments, which are sensitive to the large-x region, higher-twist effects are significantly reduced by the introduction of soft gluon contributions, but they are still relevant at ${Q}^{2}\ensuremath{\sim}$ few $(\mathrm{GeV}{/c)}^{2}$ at variance with the case of the unpolarized transverse structure function of the proton. Our finding suggests that spin-dependent correlations among partons may have more impact than spin-independent ones. As a by-product, it is also shown that the Bloom-Gilman local duality is strongly violated in the region of polarized electroproduction of the $\ensuremath{\Delta}(1232)$ resonance.

On the dimension and multiplicity of local cohomology modules

AbstractThis paper is concerned with a finitely generated module M over a (commutative Noetherian) local ring R. In the case when R is a homomorphic image of a Gorenstein local ring, one can use the well-known associativity formula for multiplicities, together with local duality and Matlis duality, to produce analogous associativity formulae for the local cohomology modules of M with respect to the maximal ideal. The main purpose of this paper is to show that these formulae also hold in the case when R is universally catenary and such that all its formal fibres are Cohen–Macaulay.These formulae involve certain subsets of the spectrum of R called the pseudosupports of M; these pseudo-supports are closed in the Zariski topology when R is universally catenary and has the property that all its formal fibres are Cohen–Macaulay. However, examples are provided to show that, in general, these pseudo-supports need not be closed. We are able to conclude that the above-mentioned associativity formulae for local cohomology modules do not hold over all local rings.

Local Duality for Modules over Noetherian Commutative Rings

Some applications of the general theorem on the existence of local duality for modules over Noetherian commutative rings are given. Let $$\Lambda$$ be a Noetherian commutative ring, let $$\mathcal{M} = \left\{ \mathfrak{M} \right\}$$ be a set of maximal ideals in $$\Lambda$$ , and let $$\widehat\Lambda = \underleftarrow {\lim }\,\Lambda _\mathfrak{M} ,\Gamma \left( \Lambda \right) = \prod\limits_{\mathfrak{M} \in \mathcal{M}} {\widehat\Lambda _\mathfrak{M} }$$ . Then the category of Artinian modules is dual to the category of Noetherian modules. Several structural results are proved, including the theorem on the structure of Artinian modules over principal ideal domains. For rings of special kinds, double centralizer theorems are proved. Bibliography: 5 titles.

A VADEMECUM ON QUARK–HADRON DUALITY

We present an elementary introduction to the problem of quark–hadron duality and its practical limitations, in particular as it concerns local duality violation in inclusive B meson decays. We show that the accurate definition of duality violation elaborated over the recent years allows one to derive informative constraints on violations of local duality. The magnitude of duality violation is particularly restricted in the total semileptonic widths. This explains its strong suppression in concrete dynamical estimates. We analyze the origin of the suppression factors in a model-independent setting, including a fresh perspective on the small velocity expansion. A new potentially significant mechanism for the violation of local duality in Γ sl (B) is analyzed. Yet we conclude that the amount of duality violation in Γ sl (B) must be safely below the half percent level, with realistic estimates being actually much smaller. The violation of local duality in Γ sl (B) is thus far below the level relevant to phenomenology. We also present a cautionary note on the B→D* decay amplitude at zero recoil and show that it is much more vulnerable to violations of quark–hadron duality than Γ sl (B). A critical review of some recent literature is given. We point out that the presently limiting factor in genuinely model-independent extraction of Vcb is the precise value of the short-distance charm quark mass. We suggest a direct and precise experimental check of local quark–hadron duality in semileptonic B→ Xcℓν decays.

Cities in the developing world

Notes how rapid urbanization is transforming the developing world – creating cities, which on the one hand offer opportunities for global economic activity, but on the other hand are beset with serious local civic, economic and social problems. New networks based on information and communication technologies are increasingly being woven into the fabric of these cities supporting the connectedness of powerful groups both within the city and between cities around the world. These flows of global information and communication between powerful groups in the city involved in global economic activity coexist with intense face‐to‐face interactions at the local level. Bangalore in South India presents a major case study of this global/local interaction, being a focal point for software development in the Asian region and globally, but also beset with local problems of civic deficiencies, growing poverty and income inequality. Explores some of the issues which arise as Bangalore serves as a nexus that links global and local networks of exchange. Examines two Bangalore networks which typify global and local duality: the network of software firms located in high technology enclaves in and around the city, and the ostracised network of the slum dwellers of Bangalore, gradually being brought into mainstream discussions of governance in the city. Finds considerable similarities between global networks and local networks and outlines some of these dynamics.

MODEL INDEPEDENT EXTRACTIONS OF |Vub| FROM INCLUSIVE B DECAYS

We discuss the possibility of extracting |Vub| from various spectra of inclusive B decays, without large systematic errors which usually arise from having to model the Fermi motion of the heavy quark. This strategy can be applied to the electron energy spectrum, as well as the hadronic mass spectrum. Modulo violation of local hadron-parton duality, the theoretical error in the extraction is estimated to be less than 10%.

Comment on “Nucleon elastic form factors and local duality”

We comment on the papers ``Nucleon elastic form factors and local duality'' [Phys. Rev. D 62, 073008 (2000)] and ``Experimental verification of quark-hadron duality'' [Phys. Rev. Lett. 85, 1186 (2000)]. Our main comment is that the reconstruction of the proton magnetic form factor, claimed to be obtained from the inelastic scaling curve thanks to parton-hadron local duality, is affected by an artifact.

Reply to “Comment on ‘Nucleon elastic form factors and local duality’ ”

Recently, we extracted [Phys. Rev. D 62, 073008 (2000)] the proton magnetic form factor from duality-averaging purely inelastic nucleon resonance data. The point stressed by Simula is that this extraction at larger values of momentum transfer is dominated by an unconstrained kinematic region. We will show at which momentum transfers this point is relevant, and argue the need for additional precise nucleon resonance data.

Transnational urbanism: locating globalization

1. Introduction: The Social Construction of Urbanism:. Why Social Practices?. Why Transnational Urbanism?. Why Agency--oriented Urban Theory?. On Social Constructionism. The Architectonics Ahead. Locating Globalization. Reconstructing Urban Theory. Part I: Locating Globalization: . 2. The as Globalisma s Other: The Confines of the Master Narrative of Time--Space Compression. Beyond Technological Determinism. Cultural Reductionism. Postmodern Subjectivity, Political Fragmentation, and Identity Politics. Essentializing Class and Marginalizing Gender. The Political Geography of Difference. An Alternative View of Urban Politics. Beyond Binary Dualities. 3. The Cities Discourse: A Return to the Master Narrative?. Reconsidering the City Thesis. The Limits of Economism. Historicizing the City. The Global Governance Agenda. Urbanism: Beyond Reification. 4. Reimagining Los Angeles from the Ground Up. Mexican Transmigration to Los Angeles The Legacy of Empire. The Social Construction of Local Economic Development. Urbanism and the Ethnic Economy. Constructing and Reconstructing Koreatown. Beyond Victimization. Part II: Reconstructing Urban Theory:. 5. Re--presenting the Local: Beyond Communitarian Metaphors. Localities as Defensive Community Formations. Rethinking the Boundaries of Locality. Localities and the Politics of Difference. The Social Construction of Space as Place. Rethinking the Politics of Everyday Life. Place--Making. 6. Beyond the Postmodern City: Rethinking Ethnography for Times. Social Constructionism and Postmodern Social Inquiry. Questioning the Knower and the Known. Constructing the Subject. The Uses and Limits of Postmodern Ethnography. Hybrid Subjects in Patterned Networks. The Border Crossings of Ethnography. 7. Transnationalizing the Grassroots. The Rise of Grassroots Politics. Transnationalizing Urban Research. Beyond the Global--Local Duality. Thinking Locally and Acting Globally. Bifocal Border Crossers. The Politics of Simultaneity. The Production of Political Space. 8. From Globalization to Urbanism. The Agency of Networks. The Rise of Translocalities Questioning the Post--national Discourse. Towards a Urban Studies. Comparative Transnationalisms. Summing Up. Epilogue. 9. Epilogue: The City as Crossroads. Index.

Moments of the protonF2structure function at lowQ2

The Q^2 dependence of inclusive electron-proton scattering F_2 structure function data in both the nucleon resonance region and the deep inelastic region, at momentum transfers below 5 (GeV/c)^2, is investigated. Moments of F_2 are constructed, down to momentum transfers of Q^2 ~ 0.1 (GeV/c)^2. The second moment is only slowly varying with Q^2 down to Q^2 ~ 1 (GeV/c)^2, which is a reflection of duality. Below Q^2 of 1 (GeV/c)^2, the Q^2 dependence of the moments is predominantly governed by the elastic contribution, whereas the inelastic channels still seem governed by local duality.

Local duality, chiral supersymmetry and fermion-like formulation of non-Abelian pure gauge fields

This work generalizes the fermion-like formulation of the Maxwell theory to the non-Abelian Yang–Mills theory without matter fields. This is a new representation of the Lie algebra valued electric and magnetic fields. The resulting equations of motion are invariant under the chiral transformation. In this formulation, duality is a kind of chirality. We may also define local duality transformations in terms of space-time dependent parameters. There is an N=1 supersymmetry for the Dirac-like operator in this representation.

D– oscillations as a probe of quark–hadron duality

It is usually argued that the Standard Model predicts slow D^0-\bar D^0 oscillations with \Delta M_D, \Delta \Gamma_D < 10^{-3}*\Gamma_D$ and that New Physics can reveal itself through \Delta M_D exceeding 10^{-3}*\Gamma_D. It is believed that the bulk of the effect is due to long distance dynamics that cannot be described at the quark level. We point out that in general the OPE yields soft GIM suppression scaling only like (m_s/\mu_{hadr})^2 and even like m_s/\mu_{hadr} rather than m_s^4/m_c^4 of the simple quark box diagram. Such contributions can actually yield \Delta M_D, \Delta \Gamma_D \sim O(10^{-3})*\Gamma_D without invoking additional long distance effects. They are reasonably suppressed as long as the OPE and local duality are qualitatively applicable in the 1/m_c expansion. We stress the importance of improving the sensitivity on \Delta \Gamma_D as well as \Delta M_D in a dedicated fashion as a laboratory for analyzing the onset of quark-hadron duality and comment on the recent preliminary study on \Delta \Gamma_D by the FOCUS group.

Local Duality Predictions for x approximately 1 Structure Functions.

Recent data on the proton F2 structure function in the resonance region suggest that local quark-hadron duality works remarkably well for each of the low-lying resonances, including the elastic, to rather low values of Q2. We derive model-independent relations between structure functions at x approximately 1 and elastic electromagnetic form factors, and predict the x-->1 behavior of nucleon polarization asymmetries and the neutron to proton structure function ratios from available data on nucleon electric and magnetic form factors.

Local quark–hadron duality in structure functions

The authors examine the consequences of local duality for elastic scattering, and derive model-independent relations between structure functions at x{approximately}1 and elastic electromagnetic form factors.

Nucleon elastic form factors and local duality

Using a newly obtained sample of inclusive electron-proton scattering data in the nucleon resonance region we have extracted the proton magnetic form factor, utilizing the quark-hadron duality concept. The extraction is in good agreement with direct measurements. Similarly, utilizing quark-hadron duality, a relation can be derived between the ratio of longitudinal to transverse deep inelastic electron-proton scattering cross sections and the ratio of the electric to magnetic proton elastic form factors. Again, the extracted ratio agrees reasonably with the existing world data. This agreement is a first experimental verification of duality in the longitudinal channel, and suggests that effects of higher-twist operators are suppressed on average in both the longitudinal and transverse electron-nucleon scattering processes.

The Alexander Duality Functors and Local Duality with Monomial Support

Alexander duality is made into a functor which extends the notion for monomial ideals to any finitely generated Nn-graded module. The functors associated with Alexander duality provide a duality on the level of free and injective resolutions, and numerous Bass and Betti number relations result as corollaries. A minimal injective resolution of a module M is equivalent to the injective resolution of its Alexander dual and contains all of the maps in the minimal free resolution of M over every Zn-graded localization. Results are obtained on the interaction of duality for resolutions with cellular resolutions and lcm-lattices. Using injective resolutions, theorems of Eagon, Reiner, and Terai are generalized to all Nn-graded modules: the projective dimension of M equals the support-regularity of its Alexander dual, and M is Cohen–Macaulay if and only if its Alexander dual has a support-linear free resolution. Alexander duality is applied in the context of the Zn-graded local cohomology functors HiI(−) for squarefree monomial ideals I in the polynomial ring S, proving a duality directly generalizing local duality, which is the case when I=m is maximal. In the process, a new flat complex for calculating local cohomology at monomial ideals is introduced, showing, as a consequence, that Terai's formula for the Hilbert series of HiI(S) is equivalent to Hochster's for Hn−im(S/I).