Gravitational duality, topologically massive gravity and holographic fluids

Self-duality in Euclidean gravitational set ups is a tool for finding remarkable geometries in four dimensions. From a holographic perspective, self-duality sets an algebraic relationship between two a priori independent boundary data: the boundary energy-momentum tensor and the boundary Cotton tensor. This relationship, which can be viewed as resulting from a topological mass term for gravity boundary dynamics, survives under the Lorentzian signature and provides a tool for generating exact bulk Einstein spaces carrying, among others, nut charge. In turn, the holographic analysis exhibits perfect-fluid-like equilibrium states and the presence of non-trivial vorticity allows to show that infinite number of transport coefficients vanish.Comment: 37 page

String Theory on AdS3: Some Open Questions

String theory on curved backgrounds has received much attention on account of both its own interest, and of its relation with gauge theories. Despite the progress made in various directions, several quite elementary questions remain unanswered, in particular in the very simple case of three-dimensional anti-de Sitter space. I will very briefly review these problems, discuss in some detail the important issue of constructing a consistent spectrum for a string propagating on ADS3 plus torsion background, and comment on potential solutions.Comment: 18 pages, latex. To appear in the proceedings of the TMR European program meeting "Quantum aspects of gauge theories, supersymmetry and unification", Paris, France, 1--7 September, 1999; v2: comments and references adde

Corfu 05 lectures - part I: Strings on curved backgrounds

In these introductory lectures we summarize some basic facts and techniques about perturbative string theory (sections 1 to 6). These are further developed (sections 7 and 8) for describing string propagation in the presence of gravitational or gauge fields. We also remind some solutions of the string equations of motion, which correspond to remarkable (NS or D) brane configurations. A part II by Emilian Dudas will be devoted to orientifold constructions and applications to string model building

Gravity, strings, modular and quasimodular forms

Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ... The latter often appear as gravitational instantons i.e. as special solutions of Einstein's equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by requiring (conformal) self-duality and Bianchi IX homogeneity. In this case, a vast range of configurations exist, which exhibit interesting modular properties. Examples of other Einstein spaces, without Bianchi IX symmetry, but with similar features are also given. Finally we discuss the emergence and the role of Eisenstein series in the framework of field and string theory perturbative expansions, and motivate the need for unravelling novel modular structures.Comment: 45 pages. To appear in the proceedings of the Besse Summer School on Quasimodular Forms - 201

Gravity duals of N=2 SCFTs and asymptotic emergence of the electrostatic description

We built the first eleven-dimensional supergravity solutions with SO(2,4)xSO(3)xU(1)_R symmetry that exhibit the asymptotic emergence of an extra U(1) isometry. This enables us to make the connection with the usual electrostatics-quiver description. The solution is obtained via the Toda frame of Kahler surfaces with vanishing scalar curvature and SU(2) action.Comment: 1+15 pages, Latex, v2: few minor changes, JHEP versio

Geometric flows in Horava-Lifshitz gravity

We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature terms can have competing behavior leading to a variety of fixed points. The instantons interpolate between any two fixed points, which are vacua of topologically massive gravity with Lambda > 0, and their action is finite. Special emphasis is placed on configurations with SU(2) isometry associated with homogeneous but generally non-isotropic Bianchi IX model geometries. In this case, the combined Ricci-Cotton flow reduces to an autonomous system of ordinary differential equations whose properties are studied in detail for different couplings. The occurrence and stability of isotropic and anisotropic fixed points are investigated analytically and some exact solutions are obtained. The corresponding instantons are classified and they are all globally R x S^3 and complete spaces. Generalizations to higher-dimensional gravities are also briefly discussed.Comment: 67 pages, 16 figures; more solutions found, 1 extra figure, 1 more reference added in v2; minor typos corrected in v3 (to appear in JHEP); an acknowledgement added in v