128 research outputs found
Critical Wilson Lines in Toroidal Compactifications of Heteroric Strings
Critical values of Wilson lines and general background fields for toroidal
compactifications of heterotic string theories are constructed systematically
using Dynkin diagrams.Comment: 32 pages, LATE
New developments in special geometry
We review recent developments in special geometry, emphasizing the role of
real coordinates. In the first part we discuss the para-complex geometry of
vector and hypermultiplets in rigid Euclidean N=2 supersymmetry. In the second
part we study the variational principle governing the near horizon limit of BPS
black holes in matter-coupled N=2 supergravity and observe that the black hole
entropy is the Legendre transform of the Hesse potential encoding the geometry
of the scalar fields.Comment: 27 pages, contributed to the Handbook on Pseudo-Riemannian Geometry
and Supersymmetr
Topological Transitions and Enhancon-like Geometries in Calabi-Yau Compactifications of M-Theory
We study the impact of topological phase transitions of the internal
Calabi-Yau threefold on the space-time geometry of five-dimensional extremal
black holes and black strings. For flop transitions and SU(2) gauge symmetry
enhancement we show that solutions can always be continued and that the
behaviour of metric, gauge fields and scalars can be characterized in a model
independent way. Then we look at supersymmetric solutions which describe naked
singularities rather than geometries with a horizon. For black strings we show
that the solution cannot become singular as long as the scalar fields take
values inside the Kahler cone. For black holes we establish the same result for
the elliptic fibrations over the Hirzebruch surfaces F_0, F_1, F_2. These three
models exhibit a behaviour similar to the enhancon, since one runs into SU(2)
enhancement before reaching the apparent singularity. Using the proper
continuation inside the enhancon radius one finds that the solution is regular.Comment: 7 page
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
Effective Supergravity Actions for Conifold Transitions
We construct gauged supergravity actions which describe the dynamics of
M-theory on a Calabi-Yau threefold in the vicinity of a conifold transition.
The actions explicitly include N charged hypermultiplets descending from
wrapped M2-branes which become massless at the conifold point. While the vector
multiplet sector can be treated exactly, we approximate the hypermultiplet
sector by the non-compact Wolf spaces X(1+N). The effective action is then
uniquely determined by the charges of the wrapped M2-branes.Comment: 57 pages, no figure
Non-extremal and non-BPS extremal five-dimensional black strings from generalized special real geometry
We construct non-extremal as well as extremal black string solutions in
minimal five-dimensional supergravity coupled to vector multiplets using
dimensional reduction to three Euclidean dimensions. Our method does not assume
that the scalar manifold is a symmetric space, and applies as well to a class
of non-supersymmetric theories governed by a generalization of special real
geometry. We find that five-dimensional black string solutions correspond to
geodesics in a specific totally geodesic para-K\"ahler submanifold of the
scalar manifold of the dimensionally reduced theory, and identify the subset of
geodesics that corresponds to regular black string solutions in five
dimensions. BPS and non-BPS extremal solutions are distinguished by whether the
corresponding geodesics are along the eigendirections of the para-complex
structure or not, a characterization which carries over to non-supersymmetric
theories. For non-extremal black strings the values of the scalars at the outer
and inner horizon are not independent integration constants but determined by
certain functions of the charges and moduli. By lifting solutions from three to
four dimensions we obtain non-extremal versions of small black holes, and find
that while the outer horizon takes finite size, the inner horizon is still
degenerate.Comment: 46 page
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