A Metric for Heterotic Moduli

Heterotic vacua of string theory are realised, at large radius, by a compact threefold with vanishing first Chern class together with a choice of stable holomorphic vector bundle. These form a wide class of potentially realistic four-dimensional vacua of string theory. Despite all their phenomenological promise, there is little understanding of the metric on the moduli space of these. What is sought is the analogue of special geometry for these vacua. The metric on the moduli space is important in phenomenology as it normalises D-terms and Yukawa couplings. It is also of interest in mathematics, since it generalises the metric, first found by Kobayashi, on the space of gauge field connections, to a more general context. Here we construct this metric, correct to first order in alpha', in two ways: first by postulating a metric that is invariant under background gauge transformations of the gauge field, and also by dimensionally reducing heterotic supergravity. These methods agree and the resulting metric is Kahler, as is required by supersymmetry. Checking that the metric is in fact Kahler is quite intricate and uses the anomaly cancellation equation for the H-field, in an essential way. The Kahler potential nevertheless takes a remarkably simple form: it is Kahler potential for special geometry with the Kahler form replaced by the alpha'-corrected hermitian form.Comment: 57 pages; v2 blackboard bold font error fixed; v3 minor improvements, typos fixed, references added; v4 version for publication in CM

La fotografia como mecanismo de resistencia y su implicación en las relaciones entre el sujeto, la imagen y el espectador

El propósito de cste articulo es el de tralar de establecer el potencial de la fotografía como medio de resistencia para mujeres y feministas. Esta noción es importante porque supone de antemano un sujeto que es capaz de tener capacidad de acción y cuya intencionalidad puede ser utilizada a favor del enjambre de necesidades de muchas mujeres, ya sea como expresión personal, terapia, o en campañas educativas 0 en contra de la violencia para nombrar solo algunas. Parte de esta discusión esta basada en las ya conocidas teorías feministas sobre representación y auto-representación (egs: Kuhn, 1985; Pollock, 1990; Mulvey, 1991; Solomon-Godeau, 1991; Neumaier, 1995), y a la vez integradas a algunas interpretaciones feministas de los modelos de poder / resistencia de Foucault (Bryson, 1988; Sawicki, 1991; McNay, 1992; Bell, 1993) Sobre esta base se construye la discusión sabre las relaciones entre la subjetividad, agencia y fotografía para sugerir cómo y cuándo han ocurrido y pueden ocurrir formas de rcsistcncia. Para reforzar el argumento se mencionan a lo largo algunos usos de la autorepresentación y el papel que el cuerpo juega en estas instancias y busquedas de resistencia (como en el trabajo de Saville & Luchford,1995/96) y otras formas en que mujeres han utilizado la fotografía (como Spence, 1986, 1995; Spellce and Solomon, 1995; Green, 1995 y Simpson, 1995). Se cubrcn también algunas de las dificultades, riesgos, implicaciones y responsabilidades inherentes alas procesos dc representación y se hace mención breve de los dilemas que conllevan los procesos de intrerpretacion. Las imagencs de Saville & Luchford son discutidas con mas profundidad y en ellas se reflejan y unen los temas cubiertos a lo largo del artículo

Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and Extensions of Landau Ginzburg Theory

Recently two groups have listed all sets of weights (k_1,...,k_5) such that the weighted projective space P_4^{(k_1,...,k_5)} admits a transverse Calabi-Yau hypersurface. It was noticed that the corresponding Calabi-Yau manifolds do not form a mirror symmetric set since some 850 of the 7555 manifolds have Hodge numbers (b_{11},b_{21}) whose mirrors do not occur in the list. By means of Batyrev's construction we have checked that each of the 7555 manifolds does indeed have a mirror. The `missing mirrors' are constructed as hypersurfaces in toric varieties. We show that many of these manifolds may be interpreted as non-transverse hypersurfaces in weighted P_4's, ie, hypersurfaces for which dp vanishes at a point other than the origin. This falls outside the usual range of Landau--Ginzburg theory. Nevertheless Batyrev's procedure provides a way of making sense of these theories.Comment: 29 pages, plain TeX. Two figures submitted separately as a uuencoded file. A plot at the end of the paper requires an extended memory version of TeX. Instructions for suppressing the plot included at head of source fil

Calabi-Yau Manifolds Over Finite Fields, I

We study Calabi-Yau manifolds defined over finite fields. These manifolds have parameters, which now also take values in the field and we compute the number of rational points of the manifold as a function of the parameters. The intriguing result is that it is possible to give explicit expressions for the number of rational points in terms of the periods of the holomorphic three-form. We show also, for a one parameter family of quintic threefolds, that the number of rational points of the manifold is closely related to as the number of rational points of the mirror manifold. Our interest is primarily with Calabi-Yau threefolds however we consider also the interesting case of elliptic curves and even the case of a quadric in CP_1 which is a zero dimensional Calabi-Yau manifold. This zero dimensional manifold has trivial dependence on the parameter over C but a not trivial arithmetic structure.Comment: 75 pages, 6 eps figure

Calabi-Yau Manifolds Over Finite Fields, II

We study zeta-functions for a one parameter family of quintic threefolds defined over finite fields and for their mirror manifolds and comment on their structure. The zeta-function for the quintic family involves factors that correspond to a certain pair of genus 4 Riemann curves. The appearance of these factors is intriguing since we have been unable to `see' these curves in the geometry of the quintic. Having these zeta-functions to hand we are led to comment on their form in the light of mirror symmetry. That some residue of mirror symmetry survives into the zeta-functions is suggested by an application of the Weil conjectures to Calabi-Yau threefolds: the zeta-functions are rational functions and the degrees of the numerators and denominators are exchanged between the zeta-functions for the manifold and its mirror. It is clear nevertheless that the zeta-function, as classically defined, makes an essential distinction between Kahler parameters and the coefficients of the defining polynomial. It is an interesting question whether there is a `quantum modification' of the zeta-function that restores the symmetry between the Kahler and complex structure parameters. We note that the zeta-function seems to manifest an arithmetic analogue of the large complex structure limit which involves 5-adic expansion.Comment: Plain TeX, 50 pages, 4 eps figure

AKILES : An Approach to Automatic Knowledge Integration in Learning Expert Systems

Knowledge integration is defined here as a machine learning task from a practical point of view—by identifying the requirements that a real-world complex application domain poses on the expert system in relation to a changing world. We present our current approach to knowledge integration in an expert system, required when the structure of the physical system, the world on which the expert system operates changes. Our exemplar domain task is technical diagnosis. We test our approach on the particular architecture of MOLTKE/3, our workbench for technical diagnosis1- which integrates second-generation expert system techniques in a unique framework. Knowledge integration is seen as the task of elaborating and accomodating new information (due to structural changes) in the expert system's knowledge, maintaining consistency in the knowledge base. The main focus is towards improving the adaptability of the expert system to the structural changes. The approach is based on three principles from the adaptation process: incrementality, extensive and intensive use of domain knowledge, and focus on strategic knowledge. We discuss how AKILES’ knowledge integration task can be used to complete the modeling cycle, i.e., covering the model-evaluation step in the layout-elaboration-evaluation cycle, as defined in [13]