Schwinger pair production in AdS2

We analyze the pair production of charged particles in two-dimensional Anti-de Sitter space (AdS_2) with a constant, uniform electric field. We compute the production rate both at a semi-classical level, viewing Schwinger pair production as a tunneling event, and at the full quantum level, by extracting the imaginary part of the one-loop amplitude. In contrast to the usual Schwinger pair production in flat space, pair production in AdS_2 requires a sufficiently large electric field E^2> M^2+1/4 in order to overcome the confining effect of the AdS geometry -- put in another way, the presence of an electric field E raises the Breitenlohner-Freedman bound to M^2 > -1/4 + E^2. For E greater than this threshold, the vacuum is unstable to production of charged pairs in the bulk. We expect our results to be helpful in constructing supersymmetric AdS_2 X S^2 perturbative string vacua, which enter in the near-horizon limit of extremal charged black holes. Although the generalized Breitenlohner-Freedman bound is obeyed in these cases, production of BPS particles at threshold is possible and relevant for AdS_2 fragmentation.Comment: 23 pages, 4 figures, v2:important revision, discussion of one-loop amplitude extended, several references adde

Models for Modules

We recall the structure of the indecomposable sl(2) modules in the Bernstein-Gelfand-Gelfand category O. We show that all these modules can arise as quantized phase spaces of physical models. In particular, we demonstrate in a path integral discretization how a redefined action of the sl(2) algebra over the complex numbers can glue finite dimensional and infinite dimensional highest weight representations into indecomposable wholes. Furthermore, we discuss how projective cover representations arise in the tensor product of finite dimensional and Verma modules and give explicit tensor product decomposition rules. The tensor product spaces can be realized in terms of product path integrals. Finally, we discuss relations of our results to brane quantization and cohomological calculations in string theory.Comment: 18 pages, 6 figure

Pompoenen - biologische teelt : de teelt van A tot Z

In deze teelthandleiding wordt de teelt en de afzet van de biologische pompoen besproken. Deze teelthandleiding is tot stand gekomen als onderdeel van het project Leren met Toekomst. De auteurs, studenten aan de Christelijke Agrarische Hogeschool ,hebben deze teelthandleiding geschreven voor de biologische pompoenenteler

Notes on the Verlinde formula in non-rational conformal field theories

We review and extend evidence for the validity of a generalized Verlinde formula in particular non-rational conformal field theories. We identify a subset of representations of the chiral algebra in non-rational conformal field theories that give rise to an analogue of the relation between modular S-matrices and fusion coefficients in rational conformal field theories. To that end we review and extend the Cardy-type brane calculations in bosonic and supersymmetric Liouville theory (and its duals) as well as in the hyperbolic three-plane H3+. We analyze the three-point functions of Liouville theory and of H3+ in detail to directly identify the fusion coefficients from the operator product expansion.Comment: 29 pages, 6 figures, v2: minor corrections, PRD versio

Batalin-Vilkovisky gauge-fixing of a chiral two-form in six dimensions

We perform the gauge-fixing of the theory of a chiral two-form boson in six dimensions starting from the action given by Pasti, Sorokin and Tonin. We use the Batalin-Vilkovisky formalism, introducing antifields and writing down an extended action satisfying the classical master equation. Then we gauge-fix the three local symmetries of the extended action in two different ways.Comment: 15 pages, latex, no figures, version accepted by Class. Quant. Gra

A Superspace Formulation for the Master Equation

It is shown that the quantum master equation of the Field Antifield quantization method at one loop order can be translated into the requirement of a superfield structure for the action. The Pauli Villars regularization is implemented in this BRST superspace and the case of anomalous gauge theories is investigated. The quantum action, including Wess Zumino terms, shows up as one of the components of a superfield that includes the BRST anomalies in the other component. The example of W2 quantum gravity is also discussed.Comment: The constrained nature of standard BRST superfields and the importance of using Alfaro and Damgaard's collective fields in the superspace approach to avoid undefined superfield derivatives was emphasized. To appear in Phys. Rev. D. Latex file, 20 page