Correct Effective Potential of Supersymmetric Yang-Mills Theory on M^4\times S^1

We study an ${\cal N}=1$ supersymmetric Yang-Mills theory defined on $M^4\times S^1$. The vacuum expectation values for adjoint scalar field in vector multiplet, though important, has been overlooked in evaluating one-loop effective potential of the theory. We correctly take the vacuum expectation values into account in addition to the Wilson line phases to give an expression for the effective potential, and gauge symmetry breaking is discussed. In evaluating the potential, we employ the Scherk-Schwarz mechanism and introduce bare mass for gaugino in order to break supersymmetry. We also obtain masses for the scalars, the adjoint scalar, and the component gauge field for the $S^1$ direction in case of the SU(2) gauge group. We observe that large supersymmetry breaking gives larger mass for the scalar. This analysis is easily applied to the $M^4\times S^1/Z_2$ case.Comment: 12 pages, 1 figur

Around and around the storytelling called «ponderación», and also asking about the «boundaries» of Law

En ese debate, ambos contendores cultivan ciertas respectivas «novelas de conceptos», con base especialmente en puntos de vista tributarios de visiones ius-esencialistas: un esencialismo jurídico«razonabilista» frente a un esencialismo legalista. Así se conservan intactas también las enormes penumbras de vaguedades de ciertos conceptos fundamentales a que respectivamente recurre cada uno de aquéllos. Entonces quedan fuera de foco preguntas cruciales, señaladamente aquéllas del todo básicas que permitan examinar las cuestiones jurídicas en planos que se fijen sobre todo en la practicidad social real de las fórmulas discursivas utilizadas. Con ello el pensamiento se aleja de encarar esas cuestiones en términos capaces de someterlas a exigencias metodológicas —precisión intersubjetiva en el manejo de esos conceptos, aquilatamiento de facticidades sociales— aptas para resolver de la manera más adecuada posible, ¡en la práctica!, los conflictos que llegan a los tribunales. Especialmente se examinan esas cuestiones a propósito de ciertas postulaciones (esencialistas) en cuanto a unos supuestos «límites» netos del derecho y atribuyéndole a éste la condición (imaginaria) de constituir un sistema propiamente dicho. Por último, a tales modelos idealistas de discurso jurídico es contrapuesto aquí un posible modelo realista para los razonamientos judiciales, dirección de pensamiento orientada a poder sacar el máximo provecho de los conocimientos pertinentes suministrados por las ciencias sociales.This paper is a critical commentary on a discussion about the judicial balancing of principles. There, both contenders have raised points of view based on some «novels of concepts», specifically two essentialist conceptions of the judicial discourse: a «rationalistic» law-essentialism vs. a legalistic essentialism. In this way, such approaches also maintain large penumbras of vagueness regarding certain fundamental concepts used by these scholars. Both lines of thinking avoid approaching law matters in a manner that would subject them to more accurate methodological requirements, i. e. through intersubjective specifications regarding those concepts and paying attention to the true social effects of judges’ interpretative choices. Thereby, the very crucial questions remain generally out of focus: notably, the basic alternative issues that would make it possible to assess legal questions through more transparent modes of juridical reasoning, which will mainly highlight the real social effectiveness of the discursive formulas employed for juridical purposes. Especially examined, are certain essentialist postulations which allege that law itself has net «limits» and confer lawyer’s thinking the imaginary condition that it is properly a system. Lastly, such idealist approaches are here countered by a possible realist model for legal reasoning, which is apt to take best advantage of empirical knowledge provided by the social sciences

The Chief Option for Legal Discourses-Novels of Concepts or a Social Technology?

A menudo unos discursos jurídicos profesionales, y más señaladamente aún la amplia mayoría de los estudios de Teoría del derecho, se autoconfinan a desplegar ciertas elucidaciones cuyos alcances son apenas semántico-convencionales. Hacen abstracción («cielo» jurídico) de cuáles sean realmente las dimensiones lingüístico-pragmáticas (la «tierra») de los discursos considerados. Ello guarda llamativas similitudes con cómo la conciencia del lector de una novela se ubica ante los personajes de ésta y sus historias propias, al sumergirse sin más en la fascinación de esos relatos asumiéndolos como un mundo en sí: se trata, en ambos casos, de determinada «sintonía» mental donde la atención se concentra exclusivamente (o poco menos) en la «historia» misma contada así, pase lo que pase en la «tierra». Los «personajes» de esas iusnovelaciones son unos conceptos, cuyas «vidas» se desenvuelven en tramas de enunciados donde su credibilidad consiste en autovalidarse entre sí, circularmente, quedando así inmunizadas de tener que acreditarlos mediante contrastaciones empíricas. En cambio, cuando el razonamiento de los juristas profesionales entra bastante en contacto con la «tierra», sus discursos constituyen unos expedientes de tecnología social —ya sea más o menos adecuada como tal—.The professional legal discourses, and even more specifically the wide majority of Legal Theory studies, often confine themselves to deploy certain elucidations whose scopes are scarcely of a semantic art —thus conventional—. They intellectually move away (into a self-made legal “heaven”) from the real linguistic-pragmatic dimensions (the “earth”) of those discourses. This mental attitude shows striking similarities with the way in which anybody, when reading a novel, will be fascinated by the characters created in this book, and by these characters’ stories. In both cases, there is a mental “tuning in” where the attention remains focused only, or almost only, in the story itself. These stories are told so touchingly (into their self-made “heaven”) that they appear to be most important, regardless of whatever actually happens (in the “earth”) outside of that book. The “characters” drawn up in theoretical legal-“novels” are a set of concepts, whose “lives” develop themselves into plots of dogmatic statements; their credibility consists in validating each other circularly —thus, immunizing them from having to be proven by empirical tests. On the contrary, when the professional legal reasoning is performed in view of what really happens on “earth” (the practice of law!), these discourses may serve as a social technology —nevertheless, they could be more or be less adequate as such—

5D seesaw, flavor structure, and mass textures

In the 5D theory in which only 3 generation right-handed neutrinos are in the bulk, the neutrino flavor mixings and the mass spectrum can be constructed through the seesaw mechanism. The 5D seesaw is easily calculated just by a replacement of the Majorana mass eigenvalues, M_i, by 2 M_*tan(h)[\pi RM_i] (M_*: 5D Planck scale, R: compactification radius). The 5D features appear when the bulk mass, which induces the 4D Majorana mass, is the same as the compactification scale or larger than it. Depending on the type of bulk mass, the seesaw scales of the 3 generations are strongly split (the tan-function case) or degenerate (the tanh-function case). In the split case, the seesaw enhancement is naturally realized. The single right-handed neutrino dominance works in a simple setup, and some specific mass textures, which are just assumptions in the 4D setup, can be naturally obtained in 5 dimensions. The degenerate case is also useful for a suitable neutrino flavor structure.Comment: 15 page

Green functions and dimensional reduction of quantum fields on product manifolds

We discuss Euclidean Green functions on product manifolds P=NxM. We show that if M is compact then the Euclidean field on P can be approximated by its zero mode which is a Euclidean field on N. We estimate the remainder of this approximation. We show that for large distances on N the remainder is small. If P=R^{D-1}xS^{beta}, where S^{beta} is a circle of radius beta, then the result reduces to the well-known approximation of the D dimensional finite temperature quantum field theory to D-1 dimensional one in the high temperature limit. Analytic continuation of Euclidean fields is discussed briefly.Comment: 17 page

Gauge-Higgs Dark Matter

When the anti-periodic boundary condition is imposed for a bulk field in extradimensional theories, independently of the background metric, the lightest component in the anti-periodic field becomes stable and hence a good candidate for the dark matter in the effective 4D theory due to the remaining accidental discrete symmetry. Noting that in the gauge-Higgs unification scenario, introduction of anti-periodic fermions is well-motivated by a phenomenological reason, we investigate dark matter physics in the scenario. As an example, we consider a five-dimensional SO(5)\timesU(1)_X gauge-Higgs unification model compactified on the $S^1/Z_2$ with the warped metric. Due to the structure of the gauge-Higgs unification, interactions between the dark matter particle and the Standard Model particles are largely controlled by the gauge symmetry, and hence the model has a strong predictive power for the dark matter physics. Evaluating the dark matter relic abundance, we identify a parameter region consistent with the current observations. Furthermore, we calculate the elastic scattering cross section between the dark matter particle and nucleon and find that a part of the parameter region is already excluded by the current experimental results for the direct dark matter search and most of the region will be explored in future experiments.Comment: 16 pages, 2 figure

Su rehabilitación del no-saber en la actual Teoría del Derecho

T he Dw or k i n - B lu ff : R eha b ilitatio n o f N o n - K n o w led g e as a “N e w ” T heor y o f L a w . This study offers some basic remarks on the principal m ethodolo g ical theses of Ronald Dworkin. However, it does not seek primarily to ‘refute’ him, for this indeed is unnecessary given (i) the superficial level at which his reasoning proceeds and (ii) the banal character of his conclusions. Four issues in particular are treated: ( a ) Dworkin adds virtually nothing to the existing corpus of knowledge in Legal Theory; indeed, he operates well below the level of existing knowledge (even in English ! ), essentially ignoring it and disregarding almost all the basic works dealing with the subjects he considers. ( b ) His theses are essentially based on an old commonplace, the B asic L e g al My th : “ O n e Right Answer”; and he stresses that jurists would arrive at such an answer by means of a typical rationalist fantasy, a ‘constructive model’, which derives from the mirage of a perfectly unitary system provided by the national law as a whole (“the principle of unity in law”). ( c ) His basic line of argument amounts to a rehabilitation of a naive realism for legal studies, mainly built upon the ordinary word-naturalism and the faith on a “heaven” of legal ideas (rules, principles, etc.); he commends such an approach as the ultimate method of knowing what law really is (“taking it seriously”). ( d ) It is difficult to see how Dworkin’s international renown could result from the content of his writings: essentially, it must derive, at least outside the Anglo-Saxon world, from the “Vincent effect” (the following of fashion). It is not worthwhile to add yet further observations on those “new” dresses, which have given rise to such meticulous commentaries within Vincent’s Empire; rather we should break the silence over the fact that its Emperor wears no clothes at all ! [Trad.: Prof. Bernard S. Jackson, Liverpool]El presente examen se ocupa del caso-Dworkin, visto el sorprendente eco obtenido por ese autor. Son examinadas sus tesis metodológicas , pero el objetivo central no es abocarse a “refutarlas” (resulta superfluo, dado el carácter bastante trivial de ellas mismas y el superficial nivel de los razonamientos en que las apoya), sino que aquí se trata principalmente de hacer ver cuatro puntos claves:a) Dworkin no agrega prácticamente nada al corpus mismo de conocimientos que han ido conformando la Teoría del Derecho, antes bien se queda muy por debajo de estos; en particular, ignora casi todos los planteamientos fundamentales presentados en numerosos estudios, incluso los de autores muy mencionados internacionalmente, con respecto a las cuestiones epistemológicas esenciales implicadas en las cuestiones básicas de la metodología jurídica. b) Sus ideas están fundamentalmente centradas en torno a una reiteración más del habitual Basic Legal Myth , “ one right answer”; para ello recurre a un típico ensueño racionalista (“constructive model”), montado sobre el espejismo corriente de que las respuestas jurídicas se obtendrían de un sistem a perfectamente unitario proporcionado por el derecho nacional (“the principle of unity in law”). c) Su argumentación propugna un realismo ingenuo —especialmente bajo modos del naturalismo lingüístico— combinado con la fe en un “cielo” normativista, como forma de conocer “en serio” el derecho. d) No se ve cómo la celebridad internacional de Dworkin pudiera ser consecuencia del contenido mismo de sus escritos; semejante éxito obedece esencialmente, al menos fuera del mundo académico anglosajón, al efecto Vicente (sumisión a la moda). No es cuestión, pues, de venir a agregar más observaciones de detalle sobre estas “nuevas” vestimentas, que han provocado tantos y tan meticulosos comentarios en el Imperio Vicente: ¡lo principal es romper el silencio sobre el hecho de que su Emperador se pasea desnudo

About the Non-Distinction Proposed between How Real Interpretations are «Possible» and How Some Other Ones are imaginarily «Possible». Discovering, thanks to J. A. García Amado, some brand-new (indeed very tasty) peripeteia of «geometric» reasoning that happened recently in the Kingdom of Absurdistan

El autor, al explicar por qué ciertas objeciones recibidas ante sus planteamientos de un escrito anterior (sobre «ponderación» judicial y demás) no tienen verdadera atingencia para ninguna de las tesis sostenidas allí por él mismo, señaladamente aborda determinadas cuestiones de fondo generales: improntas del geometrismo empleado como método de razonamiento todo-general; cómo se logra advertir qué sea posible en tanto que interpretación «objetiva» de textos; la diferencia radical que hay entre fijarse en unos ejemplos de interpretación imaginarios (invocados a guisa de argumentación por el «absurdo») y el considerar las interpretaciones creídas realmente; la escapatoria argumentativa de ampararse bajo ciertas «estrategias de inmunización» (tales como rehusarse a considerar citas opuestas del autor criticado y evitar ocuparse de aproximaciones «complejas» al tema considerado) Ésos son expedientes, muy habituales, para obviar las interrogantes claves de precisión analítico-realista que permiten detectar cuáles son los alcances verdaderos de las bases de pensamiento utilizadas.The author answers some objections concerning certain issues he stated in a former study (about judicial «balancing», etc.). He holds that these objections do not have a true pertinence to his own propositions. So he tackles certain general capital issues such as, among others: «geometrism» used as an all-general method of reasoning; how we perceive what is «possible» for «objective» interpretation of texts; the radical difference between some imaginary interpretations (used as a «reduction to absurdity») and the interpretations believed in reality; some argumentative mechanisms to «escape» uncomfortable questions by using certain «immunization strategies» of thought (such as refusing to consider any opposite quotations and avoiding to examine «complex» approaches). Those are some common ways of looking away from the cardinal analytical-realistic questions that gauge the true reach of their thinking bases