Special geometry, black holes and Euclidean supersymmetry

We review recent developments in special geometry and explain its role in the theory of supersymmetric black holes. To make this article self-contained, a short introduction to black holes is given, with emphasis on the laws of black hole mechanics and black hole entropy. We also summarize the existing results on the para-complex version of special geometry, which occurs in Euclidean supersymmetry. The role of real coordinates in special geometry is illustrated, and we briefly indicate how Euclidean supersymmetry can be used to study stationary black hole solutions via dimensional reduction over time. This article is an updated and substantially extended version of the previous review article `New developments in special geometry', hep-th/0602171.Comment: 39 pages, Contribution to the Handbook on Pseudo-Riemannian Geometry and Supersymmtry, ed. V. Corte

Duality and black hole partition functions

Supersymmetric black holes provide an excellent theoretical laboratory to test ideas about quantum gravity in general and black hole entropy in particular. When four-dimensional supergravity is interpreted as the low-energy approximation of ten-dimensional string theory or eleven-dimensional M-theory, one has a microscopic description of the black hole which allows one to count microstates and to compare the result to the macroscopic (geometrical) entropy. Recently it has been conjectured that there is a very direct connection between the partition function of the topological string and a partition function for supersymmetric black holes. We review this idea and propose a modification which makes it compatible with electric-magnetic duality.Comment: 5 pages, based on talk given at the 11th Marcel Grossmann meeting, Berlin, July 23-29, 200

Effective Actions near Singularities

We study the heterotic string compactified on K3 x T^2 near the line T=U, where the effective action becomes singular due to an SU(2) gauge symmetry enhancement. By `integrating in' the light W^\pm vector multiplets we derive a quantum corrected effective action which is manifestly SU(2) invariant and non-singular. This effective action is found to be consistent with a residual SL(2,Z) quantum symmetry on the line T=U. In an appropriate decompactification limit, we recover the known SU(2) invariant action in five dimensions.Comment: 33 pages, LaTeX. v2: cosmetic correction on titlepage. v3: references and note adde

The effects of inhomogeneities on the cosmology of type IIB conifold transitions

In this paper we examine the evolution of the effective field theory describing a conifold transition in type IIB string theory. Previous studies have considered such dynamics starting from the cosmological approximation of homogeneous fields, here we include the effects of inhomogeneities by using a real-time lattice field theory simulation. By including spatial variations we are able to simulate the effect of currents and the gauge fields which they source. We identify two different regimes where the inhomogeneities have opposite effects, one where they aid the system to complete the conifold transition and another where they hinder it. The existence of quantized fluxes in related systems has lead to the speculation that (unstable) string solutions could exist, using our simulations we give strong evidence that these string-like defects do not form.Comment: 11 pages, 2 figures. Published versio

Supergravity on R4 x S1/Z2 and singular Calabi-Yaus

We discuss the moduli space singularities that are generally present in five-dimensional vector-coupled supergravity on a spactime of the form R4 x S1/Z2, with vector fields surviving on the Z2 fixed planes. The framework of supergravity is necessarily ambiguous when it comes to the non-singular embedding theory, so we focus on those models coming from Calabi-Yau three-folds with wrapped membranes.Comment: 13 p

The role of toll-like receptors (TLRs) in bacteria-induced maturation of murine dendritic cells (DCs) - Peptidoglycan and lipoteichoic acid are inducers of DC maturation and require TLR2

Toll-like receptors (TLRs) have been found to be key elements in pathogen recognition by the host immune system. Dendritic cells (DCs) are crucial for both innate immune responses and initiation of acquired immunity. Here we focus on the potential involvement of TLR ligand interaction in DC maturation. TLR2 knockout mice and mice carrying a TLR4 mutation (C3H/HeJ) were investigated for DC maturation induced by peptidoglycan (PGN), lipopolysaccharide (LPS), or lipoteichoic acids (LTAs). All stimuli induced maturation of murine bone marrow-derived DCs in control mice. TLR2− /− mice lacked maturation upon stimulation with PGN, as assessed by expression of major histocompatibility complex class II, CD86, cytokine, and chemokine production, fluorescein isothiocyanate-dextran uptake, and mixed lymphocyte reactions, while being completely responsive to LPS. A similar lack of maturation was observed in C3H/HeJ mice upon stimulation with LPS. DC maturation induced by LTAs from two different types of bacteria was severely impaired in TLR2− /−, whereas C3H/HeJ mice responded to LTAs in a manner similar to wild-type mice. We demonstrate that DC maturation is induced by stimuli from Gram-positive microorganisms, such as PGN and LTA, with similar efficiency as by LPS. Finally, we provide evidence that TLR2 and TLR4 interaction with the appropriate ligand is essential for bacteria-induced maturation of DCs

Moduli Stabilization with the String Higgs Effect

We review the notion of the Higgs effect in the context of string theory. We find that by including this effect in time dependent backgrounds, one is led to a natural mechanism for stabilizing moduli at points of enhanced gauge symmetry. We consider this mechanism for the case of the radion (size of the extra dimensions) and find that as decompactification of the large spatial dimensions takes place the radion will remain stabilized at the self dual radius. We discuss how this mechanism can be incorporated into models of string cosmology and brane inflation to resolve some outstanding problems. We also address some issues regarding which string states should be included when constructing low energy actions in string cosmology.Comment: 20 pages, references added, typos correcte

Cosmological Solutions, a New Wick-Rotation, and the First Law of Thermodynamics

We present a modified implementation of the Euclidean action formalism suitable for studying the thermodynamics of a class of cosmological solutions containing Killing horizons. To obtain a real metric of definite signature, we perform a `triple Wick-rotation' by analytically continuing all space-like directions. The resulting Euclidean geometry is used to calculate the Euclidean on-shell action, which defines a thermodynamic potential. We show that for the vacuum de Sitter solution, planar solutions of Einstein-Maxwell theory and a previously found class of cosmological solutions of N = 2 supergravity, this thermodynamic potential can be used to define an internal energy which obeys the first law of thermodynamics. Our approach is complementary to, but consistent with the isolated horizon formalism. For planar Einstein-Maxwell solutions, we find dual solutions in Einstein-anti-Maxwell theory where the sign of the Maxwell term is reversed. These solutions are planar black holes, rather than cosmological solutions, but give rise, upon a standard Wick-rotation to the same Euclidean action and thermodynamic relations