Hessian geometry and the holomorphic anomaly

We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries a deformed version of special Kahler geometry which we characterise. The holomorphic anomaly equation arises in this framework from the integrability condition for the existence of a Hesse potential.Comment: 43 pages. Revised version: minimal changes. Final version, accepted for publication by JHE

The N=1 effective actions of D-branes in Type IIA and IIB orientifolds

We discuss the four-dimensional N=1 effective actions of single space-time filling Dp-branes in general Type IIA and Type IIB Calabi-Yau orientifold compactifications. The effective actions depend on an infinite number of normal deformations and gauge connection modes. For D6-branes the N=1 Kaehler potential, the gauge-coupling function, the superpotential and the D-terms are determined as functions of these fields. They can be expressed as integrals over chains which end on the D-brane cycle and a reference cycle. The infinite deformation space will reduce to a finite-dimensional moduli space of special Lagrangian submanifolds upon imposing F- and D-term supersymmetry conditions. We show that the Type IIA moduli space geometry is captured by three real functionals encoding the deformations of special Lagrangian submanifolds, holomorphic three-forms and Kaehler two-forms of Calabi-Yau manifolds. These elegantly combine in the N=1 Kaehler potential, which reduces after applying mirror symmetry to the results previously determined for space-time filling D3-, D5- and D7-branes. We also propose general chain integral expressions for the Kaehler potentials of Type IIB D-branes.Comment: 61 pages, v2: typos corrected and refs adde

Duality Symmetries and Supersymmetry Breaking in String Compactifications

We discuss the spontaneous supersymetry breaking within the low-energy effective supergravity action of four-dimensional superstrings. In particular, we emphasize the non-universality of the soft supersymmetry breaking parameters, the $\mu$-problem and the duality symmetries.Comment: (invited talk to the 27th ICHEP, Glasgow, July 1994), 11 page

Perturbative and non-perturbative monodromies in N=2 heterotic string vacua

In this talk we summarise our recent results on perturbative and non-perturbative monodromies in four-dimensional heterotic strings with $N=2$ space-time supersymmetry, and we compare our results with the rigid $SU(2)$ $N=2$ Yang-Mills monodromies.Comment: 6 pages, latex using espcrc2. Based on Talks given at the 29th International Symposium on the Theory of Elementary Particles, Buckow, August 1995 and at the 5th Hellenic School and Workshop on Elementary Particle Physics, Corfu, September 199

Deviations from the Area Law for Supersymmetric Black Holes

We review modifications of the Bekenstein-Hawking area law for black hole entropy in the presence of higher-derivative interactions. In four-dimensional N=2 compactifications of string theory or M-theory these modifications are crucial for finding agreement between the macroscopic entropy obtained from supergravity and the microscopic entropy obtained by counting states in string or M-theory. Our discussion is based on the effective Wilsonian action, which in the context of N=2 supersymmetric theories is defined in terms of holomorphic quantities. At the end we briefly indicate how to incorporate non-holomorphic corrections.Comment: 18 pages, LaTeX, Contribution to the Proceedings of the 32nd Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, September 1-5, 1998; a typo correcte

On the Duality between the Heterotic String and F-Theory in 8 Dimensions

In this note we compare the moduli spaces of the heterotic string compactified on a two-torus and F-Theory compactified on an elliptic K3 surface for the case of an unbroken E8 x E8 gauge group. The explicit map relating the deformation parameters alpha and beta of the F-Theory K3 surface to the moduli T and U of the heterotic torus is found using the close relationship between the K3 discriminant and the discriminant of the Calabi-Yau-threefold X(1,1,2,8,12)[24] in the limit of a large base P1.Comment: 10 pages, LaTe

Citizenship education in England 2001-2010 : young people's practices and prospects for the future : the eighth and final report from the Citizenship Education Longitudinal Study (CELS)

On the one hand, there has been a marked and steady increase in young people’s civic and political participation and indications that these young people will continue to participate as adult citizens. In contrast, there has been a hardening of attitudes toward equality and society, a weakening of attachment to communities and fluctuating levels of engagement, efficacy and trust in the political arena. The factors that shape young people’s citizenship outcomes include age and life-stage, background factors, prior citizenship outcomes, as well as levels of ‘received’ citizenship education