Constitutive relations, off shell duality rotations and the hypergeometric form of Born-Infeld theory

We review equivalent formulations of nonlinear and higher derivatives theories of electromagnetism exhibiting electric-magnetic duality rotations symmetry. We study in particular on shell and off shell formulations of this symmetry, at the level of action functionals as well as of equations of motion. We prove the conjecture that the action functional leading to Born-Infeld nonlinear electromagnetism, that is duality rotation invariant off shell and that is known to be a root of an algebraic equation of fourth order, is a hypergeometric function.Comment: 20 pages. Contribution to the proceedings of the conference BUDS2013, Frascat

New approach to nonlinear electrodynamics: dualities as symmetries of interaction

We elaborate on the duality-symmetric nonlinear electrodynamics in a new formulation with auxiliary tensor fields. The Maxwell field strength appears only in bilinear terms of the corresponding generic Lagrangian, while the self-interaction is presented by a function E depending on the auxiliary fields. Two types of dualities inherent in the nonlinear electrodynamics models admit a simple off-shell characterization in terms of this function. In the standard formulation, the continuous U(1) duality symmetry is nonlinearly realized on the Maxwell field strength. In the new setting, the same symmetry acts as linear U(1) transformations of the auxiliary field variables. The nonlinear U(1) duality condition proves to be equivalent to the linear U(1) invariance of the self-interaction E. The discrete self-duality (or self-duality by Legendre transformation) amounts to a weaker reflection symmetry of E. For a class of duality- symmetric Lagrangians we introduce an alternative representation with the auxiliary scalar field and find new explicit examples of such systems.Comment: Latex file, 21 page

Making Ends Meet: String Unification and Low-Energy Data

A long-standing problem in string phenomenology has been the fact that the string unification scale disagrees with the GUT scale obtained by extrapolating low-energy data within the framework of the minimal supersymmetric standard model (MSSM). In this paper we examine several effects that may modify the minimal string predictions and thereby bring string-scale unification into agreement with low-energy data. These include heavy string threshold corrections, non-standard hypercharge normalizations, light SUSY thresholds, intermediate gauge structure, and thresholds arising from extra matter beyond the MSSM. We explicitly evaluate these contributions within a variety of realistic free-fermionic string models, including the flipped SU(5), SO(6) x SO(4), and various SU(3) x SU(2) x U(1) models, and find that most of these sources do not substantially alter the minimal string predictions. Indeed, we find that the only way to reconcile string unification with low-energy data is through certain types of extra matter. Remarkably, however, many of the realistic string models contain precisely this required matter in their low-energy spectra.Comment: 10 pages, standard LaTeX, 1 figure (Encapsulated PostScript), version published in Phys. Rev. Lett. 75 (1995) 264

A practical approach to estimate resting energy expenditure in frail elderly people

Objectives: Some prediction equations of resting energy expenditure (REE) are available and can be used in clinical wards to determine energy requirements of patients. The aim of the present study was to assess the accuracy of those equations in sick elderly patients, using the Bland & Altman methods with our database of 187 REE measurements.Design: The 3 equations tested were Harris & Benedict equation of 1919, WHO/FAO/UNU equation of 1985 and Fredrix et al. equation of 1990. In addition, three models developed from the present data were tested.Results: The present study shows that the Fredrix et al equation gave an accurate prediction of REE without significant bias along the whole range of REE. It also shows that under-weight sick elderly patients (BMI ≤ 21 kg/m2) had a greater weight-adjusted REE than their normal weight counterparts.Conclusion: A simple formula using a factor multiplying body weight, i.e. 22 kcal/kg/d in under-weight and 19 kcal/kg/d in normal weight sick elderly was accurate to predicting REE and bias was not influenced by the level of REE. This model included half of the group in the range of ±10% of the difference between predicted REE and measured REE, but the confidence interval of the bias was ±400 kcal/d. Conversely, the Harris & Benedict and WHO formulae did accurately predict REE

Gravity duals of 2d supersymmetric gauge theories

We find new supergravity solutions generated by D5-branes wrapping a four-cycle and preserving four and two supersymmetries. We first consider the configuration in which the fivebranes wrap a four-cycle in a Calabi-Yau threefold, which preserves four supersymmetries and is a gravity dual to the Coulomb branch of two-dimensional gauge theories with N=(2,2) supersymmetry. We also study the case of fivebranes wrapping a co-associative four-cycle in a manifold of G_2-holonomy, which provides a gravity dual of N=(1,1) supersymmetric Yang-Mills theory in two dimensions. We also discuss the addition of unquenched fundamental matter fields to these backgrounds and find the corresponding gravity solutions with flavor brane sources.Comment: 34 pages + appendices; v2: minor improvement

On the Interacting Chiral Gauge Field Theory in D=6 and the Off-Shell Equivalence of Dual Born-Infeld-Like Actions

A canonical action describing the interaction of chiral gauge fields in D=6 Minkowski space-time is constructed. In a particular partial gauge fixing it reduces to the action found by Perry and Schwarz. The additional gauge symmetries are used to show the off-shell equivalence of the dimensional reduction to D=5 Minkowski space-time of the chiral gauge field canonical action and the Born-Infeld canonical action describing an interacting D=5 Abelian vector field. Its extension to improve the on-shell equivalence arguments of dual D-brane actions to off-shell ones is discussed.Comment: 18 page