Seminário de Teoria de Cordas  

Supersymmetry enhancement at the horizon of BPS black holes and rings in five space-time dimensions with eight supersymmetries, imposes stringent conditions on the fields and the geometry. For example, the BPS near-horizon geometry follows irrespective of the details of the Lagrangian. From the horizon behaviour alone the entropy and the attractor equations are derived. For spinning black holes, the results only partially agree with previous work, where additional input was used beyond the near-horizon data. In particular, the results fail to agree with four-dimensional results in the presence of higher-derivative interactions. Arguments are presented for this discrepancy. For the black rings, the horizon behavior leads to results which are consistent with the four-dimensional case, although subtle issues remain.

The old suggestive observation that black holes often resemble lumps of fluid has recently been taken beyond the level of an analogy to a precise duality. We investigate aspects of this duality, and in particular clarify the relation between area minimization of the fluid versus area maximization of the black hole horizon, and the connection between surface tension and curvature of the fluid, and surface gravity of the black hole. We also argue that the Rayleigh-Plateau instability in a fluid tube is the holographic dual of the Gregory-Laflamme instability of a black string. Associated with this fluid instability there is a rich variety of phases of fluid solutions that we study in detail, including in particular the effects of rotation. We compare them against the known results for asymptotically flat black holes finding remarkable agreement. Furthermore, we use our fluid results to discuss the unknown features of the gravitational system. Finally, we also discuss the instability of rotating plasma balls and the dual black hole interpretation.

Gauge theories with gauge potential that is an abelian 2-form or  3-form are relatively well understood and are relevant in supergravity and in string theory. We study the nonabelian version of  these gauge theories, in particular  their underlying geometry. We see that a relaxed version of  the notion of connection one form on a principal bundle is  necessary in the context of nonabelian gerbes. We then give evidence that such nonabelian gerbes are relevant for the description of a stack of M5-branes in M-theory.

Video Seminar @ KITP

Ref. Hirosi Ooguri, Masahito Yamazaki, 0811.2801v2

The OSV conjecture (2004) states that microstates of four-dimensional supersymmetric black holes are captured by the topological string, by relating the black hole partition function to the topological string partition function. Duality covariance, however, is not manifest in the OSV proposal. We show how the inclusion of a non-trivial integration measure factor restores duality covariance. Our proposal is in agreement with recent results for microstate degeneracies, and it also points to the existence of a consistent non-holomorphic deformation of special geometry.

Video Seminar @ msri

Video Seminar @ msri

The supersymmetry constraints of minimal gauged supergravity are analysed with the purpose of finding the most general asymptotically AdS_5 black holes with a topologically spherical horizon. We show that under general arguments, such black holes are essentially determined by a two dimensional space, whose curvature obeys a 4th order differential equation. We recast the problem of finding solutions of such equation as a variational problem, and show that an infinite class of solutions exists, with each solution being characterised by the number and strength of conical singularities as well as the mean squared curvature of the 2D space.

Video Seminar @ msri

Open-Closed String duality is one of the central ideas in String theory which is responsible for several striking conjectures such as the AdS/CFT. We will argue that Strebel differentials play a very natural role in implementing this duality bringing one to closer to a general understanding of gauge theories as string theories.

Video Talk @ msri

Chern-Simons gauge theory on a three-manifold M bears an intimate physical relationship to both the open and the closed Gromov-Witten theories. One surprising aspect of this relationship is that the latter theories are cohomological in character, whereas a corresponding cohomological description of Chern-Simons theory is not generally known (nor expected). Nevertheless, as I will explain, in the case that M admits a locally-free U(1) action, some observables in Chern-Simons theory do admit a cohomological description on the moduli space of flat connections on M.

Gravity in three dimensions strikes a balance between models that are tractable and models that are relevant. It may exhibit black hole solutions, graviton modes and asymptotically Anti-deSitter solutions. There have been great efforts in trying to quantize 3D gravity, but the results remain unsatisfactory. In this talk we review a recent approach to 3D gravity called "chiral gravity". This model has peculiar features giving some hope that it is particularly simple to quantize. However, there has been a sometimes heated debate regarding the stability of the model. We explain why, and give an updated status report.

Video Talk @ MSRI, 2006

A new point of view on the calculation of the exact spectrum of two dimensional sigma models in finite volume is presented. We will start from the bootstrap S-matrix, asymptotic Bethe ansatz equations, pass through the construction of bound states and Y-system (TBA), and finally use the integrable T-system (Hirota equation) to end up with convenient Destri-de-Vega-like integral equations to solve the problem numerically. The approach will be demonstrated on the $O(4)$-sigma model.

Large black holes in an asymptotically Anti-de Sitter spacetime have a dual description in terms of approximately thermal states in the boundary CFT. The reflecting boundary conditions of AdS prevent such black holes from evaporating completely. However, this situation is not ideal for the formulation of the black hole information paradox, which requires the ability of the black hole to evaporate. This can be accomplished by making the boundary of AdS partially absorptive, corresponding to a particular deformation of the gauge theory in view of the AdS/CFT correspondence. I will discuss a simple construction that produces the necessary changes on the boundary conditions. The model couples a scalar field in 1+1 dimensions to a scalar field on AdS. The interaction is localized at the boundary and leads to partial transmission into the auxiliary space. Evaporation of the large black hole corresponds to cooling down the CFT by transferring energy to an external sector. 

Recently, several new techniques have been developed which allow one to much more efficiently calculate scattering amplitudes in gauge theories. The general lesson from these techniques seems to be that for gauge theories, Feynman diagram expansions are often not the most efficient tool to calculate scattering amplitudes. Instead, one should use structures such as the helicity configuration of the amplitude and analyticity in the external momenta. In this talk, I discuss how many of these observations carry over directly from gauge theories to open string theory, and how they can be used to calculate alpha'-corrections to effective field theory amplitudes. It turns out that, viewed as an effective quantum field theory, open string theory may actually be much simpler and more elegant than one would expect.

Video talk: Colloquium by Dijkgraaf @ KITP 2008 Mathematics and the Quantum Universe

We review recently introduced geometric tools used to characterize supersymmetric flux backgrounds, with special emphasis on Generalised Complex Geometry as developed by Hitchin. We then proceed to describe Exceptional Generalised Geometry, an extension of the latter formalism based on the exceptional Lie group $E_7(7)$ which achieves a full geometrization of all fluxes, including Ramond-Ramond fluxes. First we present the formal structure of the theory: the Exceptional Generalized Tangent bundle endowed with a non-trivial twisted topology and a corresponding gerbe structure, an  Exceptional Courant bracket and an Exceptional Generalized Metric in which the bosonic degrees of freedom of $11D$ supergravity (the traditional metric and the fluxes) enter on equal footing. We then show how this formalism may be used to rewrite part of $11D$ SUGRA in the language of $N=1$ $D=4$ supersymmetry and express the corresponding effective superpotential in a manifestly $E_7(7)$ form.

Video talks @ Strings 2002
http://www.damtp.cam.ac.uk/strings02/avt/rastelli/
http://www.damtp.cam.ac.uk/strings02/avt/taylor/

In this talk, we will briefly revise the algebraic formulation of classical and quantum physical systems in terms of C*-algebras. We will check that, in the case of atomic systems, this description is actually better motivated than the usual Dirac-von Neumann axiomatic structure of Quantum Theory, which becomes nearly inevitable in this context --except for the so-called measurement problem and the reduction of the wave packet, concerning the interaction between the quantum system and the measuring apparatus, which will be briefly analyzed.