Relating Green-Schwarz and Extended Pure Spinor Formalisms by Similarity Transformation

In order to gain deeper understanding of pure-spinor-based formalisms of superstring, an explicit similarity transformation is constructed which provides operator mapping between the light-cone Green-Schwarz (LCGS) formalism and the extended pure spinor (EPS) formalism, a recently proposed generalization of the Berkovits' formalism in an enlarged space. By applying a systematic procedure developed in our previous work, we first construct an analogous mapping in the bosonic string relating the BRST and the light-cone formulations. This provides sufficient insights and allows us to construct the desired mapping in the more intricate case of superstring as well. The success of the construction owes much to the enlarged field space where pure spinor constraints are removed and to the existence of the ``B-ghost'' in the EPS formalism.Comment: 37pages, no figur

A New First Class Algebra, Homological Perturbation and Extension of Pure Spinor Formalism for Superstring

Based on a novel first class algebra, we develop an extension of the pure spinor (PS) formalism of Berkovits, in which the PS constraints are removed. By using the homological perturbation theory in an essential way, the BRST-like charge $Q$ of the conventional PS formalism is promoted to a bona fide nilpotent charge $\hat{Q}$, the cohomology of which is equivalent to the constrained cohomology of $Q$. This construction requires only a minimum number (five) of additional fermionic ghost-antighost pairs and the vertex operators for the massless modes of open string are obtained in a systematic way. Furthermore, we present a simple composite "$b$-ghost" field $B(z)$ which realizes the important relation $T(z) = \{\hat{Q}, B(z)\}$, with $T(z)$ the Virasoro operator, and apply it to facilitate the construction of the integrated vertex. The present formalism utilizes U(5) parametrization and the manifest Lorentz covariance is yet to be achieved.Comment: 38 pages, no figure. Proof of triviality of delta-homology improved and a reference adde

Using accelerometry to quantify prey attack and handling behaviours in piscivorous pike Esox lucius

Accelerometer technology was used to evaluate behaviours in the teleost ambush predator pike Esox lucius foraging on crucian carp Carassius carassius. Automated rule-based estimates of prey-size determined handling time were obtained and are compared with video-recorded behaviours. Solutions to tag attachment and the limitations imposed by battery-time and data-logging capacities are evaluated

Covariant Quantization of Superstrings Without Pure Spinor Constraints

We construct a covariant quantum superstring, extending Berkovits' approach by introducing new ghosts to relax the pure spinor constraints. The central charge of the underlying Kac-Moody algebra, which would lead to an anomaly in the BRST charge, is treated as a new generator with a new b-c system. We construct a nilpotent BRST current, an anomalous ghost current and an anomaly-free energy-momentum tensor. For open superstrings, we find the correct massless spectrum. In addition, we construct a Lorentz invariant B-field to be used for the computation of the integrated vertex operators and amplitudes.Comment: 30 page

Membranes for Topological M-Theory

We formulate a theory of topological membranes on manifolds with G_2 holonomy. The BRST charges of the theories are the superspace Killing vectors (the generators of global supersymmetry) on the background with reduced holonomy G_2. In the absence of spinning formulations of supermembranes, the starting point is an N=2 target space supersymmetric membrane in seven euclidean dimensions. The reduction of the holonomy group implies a twisting of the rotations in the tangent bundle of the branes with ``R-symmetry'' rotations in the normal bundle, in contrast to the ordinary spinning formulation of topological strings, where twisting is performed with internal U(1) currents of the N=(2,2) superconformal algebra. The double dimensional reduction on a circle of the topological membrane gives the strings of the topological A-model (a by-product of this reduction is a Green-Schwarz formulation of topological strings). We conclude that the action is BRST-exact modulo topological terms and fermionic equations of motion. We discuss the role of topological membranes in topological M-theory and the relation of our work to recent work by Hitchin and by Dijkgraaf et al.Comment: 22 pp, plain tex. v2: refs. adde

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

We present a group theoretical study of the symmetry-broken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N-electron single quantum dot (with and without an external magnetic field). The breaking of rotational symmetry results in canonical orbitals that (1) are associated with the eigenvectors of a Hueckel hamiltonian having sites at the positions determined by the equilibrium molecular configuration of the classical N-electron problem, and (2) transform according to the irreducible representations of the point group specified by the discrete symmetries of this classical molecular configuration. Through restoration of the total-spin and rotational symmetries via projection techniques, we show that the point-group discrete symmetry of the unrestricted Hartree-Fock wave function underlies the appearance of magic angular momenta (familiar from exact-diagonalization studies) in the excitation spectra of the quantum dot. Furthermore, this two-step symmetry-breaking/symmetry-restoration method accurately describes the energy spectra associated with the magic angular momenta.Comment: A section VI.B entitled "Quantitative description of the lowest rotational band" has been added. 16 pages. Revtex with 10 EPS figures. A version of the manuscript with high quality figures is available at http://calcite.physics.gatech.edu/~costas/uhf_group.html For related papers, see http://www.prism.gatech.edu/~ph274c

There and back again: migration in freshwater fishes

Animal migration is an amazing phenomenon that has fascinated humans for long. Many freshwater fishes also show remarkable migrations, whereof the spectacular mass migrations of salmonids from the spawning streams are the most well known and well studied. However, recent studies have shown that migration occurs in a range of freshwater fish taxa from many different habitats. In this review we focus on the causes and consequences of migration in freshwater fishes. We start with an introduction of concepts and categories of migration, and then address the evolutionary causes that drive individuals to make these migratory journeys. The basis for the decision of an individual fish to migrate or stay resident is an evaluation of the costs and benefits of different strategies to maximize its lifetime reproductive effort. We provide examples by discussing our own work on the causes behind seasonal migration in a cyprinid fish, roach (Rutilus rutilus (L., 1758)), within this framework. We then highlight different adaptations that allow fish to migrate over sometimes vast journeys across space, including capacity for orientation, osmoregulation, and efficient energy expenditure. Following this we consider the consequences of migration in freshwater fish from ecological, evolutionary, and conservation perspectives, and finally, we detail some of the recent developments in the methodologies used to collect data on fish migration and how these could be used in future research

The cohomology of superspace, pure spinors and invariant integrals

The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to \a'^3. Some partial results on $N=2,d=10$ and $N=1,d=11$ are also given.Comment: 24 pages. Minor changes; added reference

Enhanced T-odd P-odd Electromagnetic Moments in Reflection Asymmetric Nuclei

Collective P- and T- odd moments produced by parity and time invariance violating forces in reflection asymmetric nuclei are considered. The enhanced collective Schiff, electric dipole and octupole moments appear due to the mixing of rotational levels of opposite parity. These moments can exceed single-particle moments by more than two orders of magnitude. The enhancement is due to the collective nature of the intrinsic moments and the small energy separation between members of parity doublets. In turn these nuclear moments induce enhanced T- and P- odd effects in atoms and molecules. First a simple estimate is given and then a detailed theoretical treatment of the collective T-, P- odd electric moments in reflection asymmetric, odd-mass nuclei is presented and various corrections evaluated. Calculations are performed for octupole deformed long-lived odd-mass isotopes of Rn, Fr, Ra, Ac and Pa and the corresponding atoms. Experiments with such atoms may improve substantially the limits on time reversal violation.Comment: 28 pages, Revte