Homologies of Algebraic Structures via Braidings and Quantum Shuffles

In this paper we construct "structural" pre-braidings characterizing different algebraic structures: a rack, an associative algebra, a Leibniz algebra and their representations. Some of these pre-braidings seem original. On the other hand, we propose a general homology theory for pre-braided vector spaces and braided modules, based on the quantum co-shuffle comultiplication. Applied to the structural pre-braidings above, it gives a generalization and a unification of many known homology theories. All the constructions are categorified, resulting in particular in their super- and co-versions. Loday's hyper-boundaries, as well as certain homology operations are efficiently treated using the "shuffle" tools

Role of Fourier Modes in Finite-Size Scaling above the Upper Critical Dimension

Renormalization-group theory stands, since over 40 years, as one of the pillars of modern physics. As such, there should be no remaining doubt regarding its validity. However, finite-size scaling, which derives from it, has long been poorly understood above the upper critical dimension $d_c$ in models with free boundary conditions. Besides its fundamental significance for scaling theories, the issue is important at a practical level because finite-size, statistical-physics systems, with free boundaries above $d_c$, are experimentally accessible with long-range interactions. Here we address the roles played by Fourier modes for such systems and show that the current phenomenological picture is not supported for all thermodynamic observables either with free or periodic boundaries. Instead, the correct picture emerges from a sector of the renormalization group hitherto considered unphysical.Comment: 10 pages, 2 figure

Transnational lives and their boundaries : expatriates in Jakarta, Indonesia

This thesis investigates the lives of Euro-Americans expatriates, who are posted by multinational companies for a period between 1 to 5 years to the city of Jakarta, Indonesia. The main argument of this thesis is that expatriates' transnational lives are marked by boundaries. The prevalence of boundaries contrasts with current discussions on migration and transnationalism, which emphasise notions of fluidity. I suggest that expatriates' construction, maintenance, and transgression of boundaries characterises their relations with Indonesia. This is played out in especially in the domains of race and gender, interconnected with the body, the use of space, and socialising. Gender and race are among the most persistent of categories, which reconfigure especially expatriate women's experience of Indonesia, although they can never quite be transcended. The centrality of these categories, of race and gender, is not reflected in research on transnationalism. I argue that although expatriates lead `transnational' lives, their practices are marked by boundaries more than by flows. The notions of flows and boundaries are not conceptualised as opposites, but as necessarily presupposing each other. I suggest, though, that the role of boundaries in transnational lives has so far been disregarded. The study of expatriates thus adds a crucial dimension to theories of transnationalism. It also carries political relevance, asexpatriates represent `transnationalism from above', counterbalancing the existing research on unskilled labour migration movements. As expatriates have hardly been investigated at all, this study then fills a significant gap in terms of ethnography

The Image of Contemporary Society in Neil Gaiman’s Neverwhere

Neil Gaiman’s urban fantasy novel Neverwhere revolves around some problematic aspects prevalent in the contemporary world, such as an iniquitous discrepancy between social classes or a problematic attitude to history. The artistic universes created by Gaiman are instrumental in conveying a complex condition of postmodern society. Although one of the represented worlds, London Above, is realistic and the other, London Below, is fantastic, both are suggestive of the contemporary social situation, citizens’ shared values and aspirations. Only when considered together can they reveal a comprehensive image of what the community accepts and what it rejects as no longer consistent with commonly held beliefs. The disparities in the representations of London Above and London Below refer to the division into the present and the past. The realistically portrayed metropolis is the embodiment of contemporary times. The fantastic London Below epitomises all that is ignored or rejected by London Above. The present study is going to discuss the main ideas encoded in the semiotic spaces created by Neil Gaiman, on the basis of postmodern theories. I am going to focus on how the characteristic features of postmodern fiction, such as the use of fantasy and the application of the ontological dominant, by highlighting the boundaries between London Above and London Below affect the general purport of the work

String Expansion as Large N Expansion of Gauge Theories

We consider string perturbative expansion in the presence of D-branes imbedded in orbifolded space-time. In the regime where the string coupling is weak and $\alpha'\to 0$, the string perturbative expansion coincides with `t Hooft's large N expansion. We specifically concentrate on theories with d=4 and ${\cal N}=0,1,2,4$, and use world-sheet orbifold techniques to prove vanishing theorems for the field theory beta functions to all orders in perturbation theory in the large N limit. This is in accord with recent predictions.Comment: 18 pages, harvmac, minor corrections and additional reference

Explicit Supersymmetry Breaking on Boundaries of Warped Extra Dimensions

Explicit supersymmetry breaking is studied in higher dimensional theories by having boundaries respect only a subgroup of the bulk symmetry. If the boundary symmetry is the maximal subgroup allowed by the boundary conditions imposed on the fields, then the symmetry can be consistently gauged; otherwise gauging leads to an inconsistent theory. In a warped fifth dimension, an explicit breaking of all bulk supersymmetries by the boundaries is found to be inconsistent with gauging; unlike the case of flat 5D, complete supersymmetry breaking by boundary conditions is not consistent with supergravity. Despite this result, the low energy effective theory resulting from boundary supersymmetry breaking becomes consistent in the limit where gravity decouples, and such models are explored in the hope that some way of successfully incorporating gravity can be found. A warped constrained standard model leads to a theory with one Higgs boson with mass expected close to the experimental limit. A unified theory in a warped fifth dimension is studied with boundary breaking of both SU(5) gauge symmetry and supersymmetry. The usual supersymmetric prediction for gauge coupling unification holds even though the TeV spectrum is quite unlike the MSSM. Such a theory may unify matter and Higgs in the same SU(5) hypermultiplet.Comment: 30 pages, version to appear in Nucl. Phys.