Abelian 2-form gauge theory: superfield formalism

We derive the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for {\it all} the fields of a free Abelian 2-form gauge theory by exploiting the geometrical superfield approach to BRST formalism. The above four (3 + 1)-dimensional (4D) theory is considered on a (4, 2)-dimensional supermanifold parameterized by the four even spacetime variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of odd Grassmannian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0, \theta \bar\theta + \bar\theta \theta = 0). One of the salient features of our present investigation is that the above nilpotent (anti-)BRST symmetry transformations turn out to be absolutely anticommuting due to the presence of a Curci-Ferrari (CF) type of restriction. The latter condition emerges due to the application of our present superfield formalism. The actual CF condition, as is well-known, is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that our present 4D Abelian 2-form gauge theory imbibes some of the key signatures of the 4D non-Abelian 1-form gauge theory. We briefly comment on the generalization of our supperfield approach to the case of Abelian 3-form gauge theory in four (3 + 1)-dimensions of spacetime.Comment: LaTeX file, 23 pages, journal versio

Sex Allocation Patterns across Cooperatively Breeding Birds Do Not Support Predictions of the Repayment Hypothesis

The repayment hypothesis predicts that reproductive females in cooperative breeding systems overproduce the helping sex. Thanks to well-documented examples of this predicted sex ratio bias, repayment has been considered an important driver of variation in sex allocation patterns. Here we test this hypothesis using data on population brood sex ratios and facultative sex allocation from 28 cooperatively breeding bird species. We find that biased sex ratios of helpers do not correlate with production biases in brood sex ratios, contrary to predictions. We also test whether females facultatively produce the helping sex in response to a deficiency of help (i.e., when they have fewer or no helpers). Although this is observed in a few species, it is not a significant trend overall, with a mean effect size close to zero. We conclude that, surprisingly, repayment does not appear to be a widespread influence on sex ratios in cooperatively breeding birds. We discuss possible explanations for our results and encourage further examination of the repayment model

Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory

We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the four (3 + 1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated (B \wedge F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci-Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion that are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-) BRST symmetry transformations.Comment: LaTeX file, 22 pages, journal versio

On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories

We demonstrate a few striking similarities and some glaring differences between (i) the free four (3 + 1)-dimensional (4D) Abelian 2-form gauge theory, and (ii) the anomalous two (1 + 1)-dimensional (2D) Abelian 1-form gauge theory, within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We demonstrate that the Lagrangian densities of the above two theories transform in a similar fashion under a set of symmetry transformations even though they are endowed with a drastically different variety of constraint structures. Taking the help of our understanding of the 4D Abelian 2-form gauge theory, we prove that the gauge invariant version of the anomalous 2D Abelian 1-form gauge theory is a new field-theoretic model for the Hodge theory where all the de Rham cohomological operators of differential geometry find their physical realizations in the language of proper symmetry transformations. The corresponding conserved charges obey an algebra that is reminiscent of the algebra of the cohomological operators. We briefly comment on the consistency of the 2D anomalous 1-form gauge theory in the language of restrictions on the harmonic state of the (anti-) BRST and (anti-) co-BRST invariant version of the above 2D theory.Comment: LaTeX file, 37 pages, version to appear in EPJ

The Large Magellanic Cloud: A power spectral analysis of Spitzer images

We present a power spectral analysis of Spitzer images of the Large Magellanic Cloud. The power spectra of the FIR emission show two different power laws. At larger scales (kpc) the slope is ~ -1.6, while at smaller ones (tens to few hundreds of parsecs) the slope is steeper, with a value ~ -2.9. The break occurs at a scale around 100-200 pc. We interpret this break as the scale height of the dust disk of the LMC. We perform high resolution simulations with and without stellar feedback. Our AMR hydrodynamic simulations of model galaxies using the LMC mass and rotation curve, confirm that they have similar two-component power-laws for projected density and that the break does indeed occur at the disk thickness. Power spectral analysis of velocities betrays a single power law for in-plane components. The vertical component of the velocity shows a flat behavior for large structures and a power law similar to the in-plane velocities at small scales. The motions are highly anisotropic at large scales, with in-plane velocities being much more important than vertical ones. In contrast, at small scales, the motions become more isotropic.Comment: 8 pages, 4 figures, talk presented at "Galaxies and their Masks", celebrating Ken Freeman's 70-th birthday, Sossusvlei, Namibia, April 2010. To be published by Springer, New York, editors D.L. Block, K.C. Freeman, & I. Puerar

Mersenne Primes, Polygonal Anomalies and String Theory Classification

It is pointed out that the Mersenne primes $M_p=(2^p-1)$ and associated perfect numbers ${\cal M}_p=2^{p-1}M_p$ play a significant role in string theory; this observation may suggest a classification of consistent string theories.Comment: 10 pages LaTe

Born reciprocity and the 1/r potential

Many structures in nature are invariant under the transformation (p,r)->(br,-p/b), where b is some scale factor. Born's reciprocity hypothesis affirms that this invariance extends to the entire Hamiltonian and equations of motion. We investigate this idea for atomic physics and galactic motion, where one is basically dealing with a 1/r potential and the observations are very accurate, so as to determine the scale $b = m\Omega$. We find that an $\Omega \sim 1.5\times 10^{-15}$ Hz has essentially no effect on atomic physics but might possibly offer an explanation for galactic rotation, without invoking dark matter.Comment: 14 pages, with 4 figures, Latex, requires epsf.tex and iop style file

Moduli Dependent mu-Terms in a Heterotic Standard Model

In this paper, we present a formalism for computing the non-vanishing Higgs mu-terms in a heterotic standard model. This is accomplished by calculating the cubic product of the cohomology groups associated with the vector bundle moduli (phi), Higgs (H) and Higgs conjugate (Hbar) superfields. This leads to terms proportional to phi H Hbar in the low energy superpotential which, for non-zero moduli expectation values, generate moduli dependent mu-terms of the form H Hbar. It is found that these interactions are subject to two very restrictive selection rules, each arising from a Leray spectral sequence, which greatly reduce the number of moduli that can couple to Higgs-Higgs conjugate fields. We apply our formalism to a specific heterotic standard model vacuum. The non-vanishing cubic interactions phi H Hbar are explicitly computed in this context and shown to contain only four of the nineteen vector bundle moduli.Comment: 23 pages, LaTe

Modeling water waves beyond perturbations

In this chapter, we illustrate the advantage of variational principles for modeling water waves from an elementary practical viewpoint. The method is based on a `relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible, and imposing some suitable subordinate constraints. This approach allows the construction of approximations without necessarily relying on a small parameter. This is illustrated via simple examples, namely the Serre equations in shallow water, a generalization of the Klein-Gordon equation in deep water and how to unify these equations in arbitrary depth. The chapter ends with a discussion and caution on how this approach should be used in practice.Comment: 15 pages, 1 figure, 39 references. This document is a contributed chapter to an upcoming volume to be published by Springer in Lecture Notes in Physics Series. Other author's papers can be downloaded at http://www.denys-dutykh.com

WIMP Annual Modulation with Opposite Phase in Late-Infall Halo Models

We show that in the late-infall model of our galactic halo by P. Sikivie the expected phase of the annual modulation of a WIMP halo signal in direct detection experiments is opposite to the one usually expected. If a non-virialized halo component due to the infall of (collisionless) dark matter particles cannot be rejected, an annual modulation in a dark matter signal should be looked for by experimenters without fixing the phase a-priori. Moreover, WIMP streams coming to Earth from directions above and below the galactic plane should be expected, with a characteristic pattern of arrival directions.Comment: 15 pages, 5 figure