The SU(2) Skyrme model and anomaly

The SU(2) Skyrme model,expanding in the collective coordinates variables, gives rise to second-class constraints. Recently this system was embedded in a more general Abelian gauge theory using the BFFT Hamiltonian method. In this work we quantize this gauge theory computing the Noether current anomaly using for this two different methods: an operatorial Dirac first class formalism and the non-local BV quantization coupled with the Fujikawa regularization procedure.Comment: 6 pages, Revtex. Final version to be published in Physics Letters

Nonlocal Regularization For Non-Abelian Gauge Theories For Arbitrary Gauge Parameter

We study the nonlocal regularization for the non-abelian gauge theories for an arbitrary value of the gauge parameter (\xi). We show that the procedure for the nonlocalization of field theories established earlier by the original authors, when applied in that form to the Faddeev-Popov effective action in a linear gauge cannot lead to a (\xi)-independent result for the observables. We then show that an alternate procedure which is simpler can be used and that it leads to the S-matrix elements (where they exist) independent of (\xi).Comment: 21 pages,postscript fil

Graded Majorana spinors

In many mathematical and physical contexts spinors are treated as Grassmann odd valued fields. We show that it is possible to extend the classification of reality conditions on such spinors by a new type of Majorana condition. In order to define this graded Majorana condition we make use of pseudo-conjugation, a rather unfamiliar extension of complex conjugation to supernumbers. Like the symplectic Majorana condition, the graded Majorana condition may be imposed, for example, in spacetimes in which the standard Majorana condition is inconsistent. However, in contrast to the symplectic condition, which requires duplicating the number of spinor fields, the graded condition can be imposed on a single Dirac spinor. We illustrate how graded Majorana spinors can be applied to supersymmetry by constructing a globally supersymmetric field theory in three-dimensional Euclidean space, an example of a spacetime where standard Majorana spinors do not exist.Comment: 16 pages, version to appear in J. Phys. A; AFK previously published under the name A. F. Schunc

Schur Q-functions and degeneracy locus formulas for morphisms with symmetries

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our description uses essentially Schur Q-polynomials of a bundle, and is based on a certain push-forward formula for these polynomials in a Grassmann bundle.Comment: 22 pages, AMSTEX, misprints corrected, exposition improved. to appear in the Proceedings of Intersection Theory Conference in Bologna, "Progress in Mathematics", Birkhause

Continuous non-perturbative regularization of QED

We regularize in a continuous manner the path integral of QED by construction of a non-local version of its action by means of a regularized form of Dirac's $\delta$ functions. Since the action and the measure are both invariant under the gauge group, this regularization scheme is intrinsically non-perturbative. Despite the fact that the non-local action converges formally to the local one as the cutoff goes to infinity, the regularized theory keeps trace of the non-locality through the appearance of a quadratic divergence in the transverse part of the polarization operator. This term which is uniquely defined by the choice of the cutoff functions can be removed by a redefinition of the regularized action. We notice that as for chiral fermions on the lattice, there is an obstruction to construct a continuous and non ambiguous regularization in four dimensions. With the help of the regularized equations of motion, we calculate the one particle irreducible functions which are known to be divergent by naive power counting at the one loop order.Comment: 23 pages, LaTeX, 5 Encapsulated Postscript figures. Improved and revised version, to appear in Phys. Rev.

Dnd knockout ablates germ cells and demonstrates germ cell independent sex differentiation in Atlantic salmon

-Introgression of farmed salmon escapees into wild stocks is a major threat to the genetic integrity of wild populations. Using germ cell-free fish in aquaculture may mitigate this problem. Our study investigated whether it is possible to produce germ cell-free salmon in F0 by using CRISPR-Cas9 to knock out dnd, a factor required for germ cell survival in vertebrates. To avoid studying mosaic animals, sgRNA targeting alb was simultaneously used as a visual tracer since the phenotype of alb KO is complete loss of pigmentation. Induced mutations for the tracer (alb) and the target (dnd) genes were highly correlated and produced germ cell-less fish lacking pigmentation, underlining the suitability of alb KO to serve as tracer for targeted double allelic mutations in F0 animals in species with prohibitively long generation times. This is also the first report describing dnd knockout in any fish species. Analyzing gene expression and histology of dnd KO fish revealed that sex differentiation of the somatic compartment does not depend on the presence of germ cells. However, the organization of the ovarian somatic compartment seems compromised in mutant fish

The BPHZ renormalised BV master equation and Two-loop Anomalies in Chiral Gravities

Anomalies and BRST invariance are governed, in the context of Lagrangian Batalin-Vilkovisky quantization, by the master equation, whose classical limit is $(S, S)=0$. Using Zimmerman's normal products and the BPHZ renormalisation method, we obtain a corresponding local quantum operator equation, which is valid to all orders in perturbation theory. The formulation implies a calculational method for anomalies to all orders that is useful also outside the BV context and that remains completely within regularised perturbation theory. It makes no difference in principle whether the anomaly appears at one loop or at higher loops. The method is illustrated by computing the one- and two-loop anomalies in chiral $W_3$ gravity.Comment: 44 pages, LaTex. 4 figures, epsf. Discussion in section 4 extended, assorted small modifications, 3 references added. As it will be published in NP

Rescue of germ cells in dnd crispant embryos opens the possibility to produce inherited sterility in Atlantic salmon

Genetic introgression of escaped farmed Atlantic salmon (Salmo salar) into wild populations is a major environmental concern for the salmon aquaculture industry. Using sterile fish in commercial aquaculture operations is, therefore, a sustainable strategy for bio-containment. So far, the only commercially used methodology for producing sterile fish is triploidization. However, triploid fish are less robust. A novel approach in which to achieve sterility is to produce germ cell-free salmon, which can be accomplished by knocking out the dead-end (dnd) gene using CRISPR-Cas9. The lack of germ cells in the resulting dnd crispants, thus, prevents reproduction and inhibits subsequent large-scale production of sterile fish. Here, we report a rescue approach for producing germ cells in Atlantic salmon dnd crispants. To achieve this, we co-injected the wild-type (wt) variant of salmon dnd mRNA together with CRISPR-Cas9 constructs targeting dnd into 1-cell stage embryos. We found that rescued one-year-old fish contained germ cells, type A spermatogonia in males and previtellogenic primary oocytes in females. The method presented here opens a possibility for large-scale production of germ-cell free Atlantic salmon offspring through the genetically sterile broodstock which can pass the sterility trait on the next generation.publishedVersio