2002 seminars

Miguel Costa, Universidade do Porto
Deeply Virtual Compton Scattering from Gauge/Gravity Duality

We use gauge/gravity duality to study deeply virtual Compton scattering (DVCS) in the limit of high center of mass energy at fixed momentum transfer, corresponding to the limit of low Bjorken $x$, where the process is dominated by the exchange of the pomeron. Using conformal Regge theory we review the form of the amplitude for pomeron exchange, both at strong and weak $'t$ Hooft coupling. At strong coupling, the pomeron is described as the graviton Regge trajectory in AdS space, with a hard wall to mimic confinement effects. This model agrees with HERA data in a large kinematical range. The behavior of the DVCS cross section for very high energies, inside saturation, can be explained by a simple AdS black disk model. In a restricted kinematical window, this model agrees with HERA data as well.

João Esteves, CAMGSD
Geometric Quantization: a beginner's perspective

Geometric Quantization is an attempt to give a rigorous mathematical formulation for the process of quantization of some physical systems, like the ones studied in Quantum Mechanics. In this first talk we review some well known facts and techniques in this framework with emphasis on the quantization of the harmonic oscillator as an explicit example. We will present some classical results on this subject that follow a geometrical perspective, in contrast with the traditional approach of solving explicitly the Schrodinger equation.

Additional file

http://www.math.ist.utl.pt/~mesteves/Geom-Quant-2012.pdf

José Mourão, CAMGSD/DMIST
Geometric quantization and simple non-equivalent quantizations of the harmonic oscilator

I will recall the basics of geometric quantization and what is usually meant by quantizing a mechanical (a hamiltonian) system.

Will then consider two one-parameter families of Kahler polarizations on the plane intersecting at one point and degenerating to two important real polarizations: the vertical or Schrodinger one and the (singular) harmonic-oscilator-energy one.

Eventhough the quantizations associated with the above real degenerations are equivalent, on the coherent-space-transform driven quantum path from one to the other [more specifically all along the half way from the crossing point to the energy representation] I will argue that the Kahler quantizations are inequivalent to the two real ones above.

Will then comment briefly on the relevance of this analysis to loop quantum gravity.

Based on joint work with William Kirwin and João P. Nunes.

Samuel Monnier, ENS Paris
Geometric quantization and the metric dependence of the self-dual field theory

We will review Witten's ideas for the construction of the partition function of the self-dual field on a Riemannian manifold $M$. Then we will explain how geometric quantization on the intermediate Jacobian of $M$ can be used to find the metric dependence of the partition function. We will also show how the local gravitational anomaly of the theory is recovered in this formalism. Applying these results to the $(2,0)$ supermultiplet on a Calabi-Yau threefold, we will show that its one-loop determinant coincides with the one-loop determinant of the B-model.

Additional file

http://arxiv.org/abs/1011.5890

Yolanda Lozano, Universidad de Oviedo
Non-singlet baryons in gauge / gravity duality

The AdS/CFT correspondence predicts the existence of non-singlet baryons, i.e. baryons with a number of quarks less than the rank of the gauge group, at strong 't Hooft coupling. Using gauge/gravity duality we will see that these configurations also exist in more realistic, less supersymmetric and/or confining, gauge theories. We will also explore their realization in the gravity side beyond the strong 't Hooft coupling regime.

João Penedones, Universidade do Porto
Conformal Regge Theory

In this talk, we will review the basic properties of the Mellin space representation of conformal correlation functions and use it to study high energy scattering in the dual string theory on Anti-de Sitter space. We shall see that this regime is dominated by the exchange of the leading Regge trajectory (i.e. leading twist fields), whose resumed contribution can be described by pomeron exchange. In the process, we will obtain new predictions for 3pt-functions involving leading twist operators.

Gaetan Borot, University of Geneva
Matrix models, non-perturbative topological recursion, and knot invariants

At least heuristically, the asymptotics of convergent matrix integrals are described by a non-perturbative version of the topological recursion, which is not in general an expansion in powers of the coupling constant $g_s$. However, if a Boutroux and a quantification condition hold (these notions will be explained), one recovers a perturbative expansion from the non-perturbative answer provided $g_s$ is quantified, and the non-perturbative effects just result in renormalizations at all orders by derivatives of theta functions. In the second part of the talk, I will explain how this framework can be used in knot theory. I will describe a Chern-Simons matrix model computation for torus knots invariants inspired by a recent work of Brini, Eynard and Marino. By generalizing to the case of hyperbolic knots (even though no matrix model is known in this case), this leads us to a conjecture (completing a former one of Dijkgraaf, Fuji and Manabe) for the all-order asymptotic expansion of the Jones polynomial of hyperbolic knots.

Michele Cirafici, CAMGSD
Line defects and framed BPS quivers

The spectrum of BPS states of \(N=2\) supersymmetric gauge theories has a subtle moduli dependence. The moduli space is divided in chambers and across chambers the spectrum jumps according to a wall-crossing formula. In certain chambers the whole spectrum can be generated via a so-called BPS quiver. We use a simple modification of this quiver to characterize line defects by studying which BPS states can form a bound state with the defect.

Pietro Grassi, Alessandria
Fluid/Gravity Correspondence: Navier-Stokes Equations from Einstein Equations

We will show how to derive the full fledged non-linear Navier-Stokes equations for a conformal fluid from the AdS/CFT correspondence. We study a new version of the this correspondence in order to take into account fermionic zero modes and we construct the full solution for Black Holes in AdS 5-dimensional spaces and we derive the fermionic corrections to Navier-Stokes equations.

João Gomes, Faculdade de Ciências, Universidade do Porto
Recent developments in computing the quantum entropy function of supersymmetric black holes and exact holography

In this talk I will review recent developments in the computation of quantum corrections to the entropy of supersymmetric black holes based on the $Ad S_2/CFT_1$ correspondence. The use of supersymmetric localization of supergravity on $Ad S_2\times S_2$ is able to reduce a path integral over string fields to a finite dimensional integral. This path integral is the quantum version of Wald's entropy. We look in particular to $1/8$ BPS black holes in four dimensional $N=8$ string theory and compare the gravity computation with the well known microscopic answer. We find exact agreement, up to much subleading non-perturbative corrections that can in principle be computed. These results go much beyond the large charge approximation and constitute a first test of exact holography.

Nicolas Orantin, Instituto Superior Técnico
Generalized loop equations and their formal solution on deformed spectral curves

Many formal matrix models have been proved to be solvable by the so-called topological recursion formalism. However, the universality of this solution was still mysterious since it had to be derived case by case. In this talk, I will explain how to solve many formal matrix models by deriving some generalized loop equations for sets of normal random matrices whose eigenvalues have an arbitrary interaction. I will show how the deformation of the interaction among eigenvalues maps to a deformation of the spectral curve associated. This talk will be mainly based on the example of loop models on random surfaces to explicit this construction. If time allows, I will also explain why this procedure can be seen as a matrix model counterpart of Givental group action in the context of Gromov-Witten theory.

Based on a joint work with G. Borot and B. Eynard.

Vitor Cardoso, CENTRA
Black hole bombs

We show that massive vector fields around rotating black holes can give rise to a strong superradiant instability which extracts angular momentum from the hole. The observation of supermassive spinning black holes imposes limits on this mechanism. We show that current supermassive black hole spin estimates provide the tightest upper limits on the mass of the photon ($m v<4 \times 10^{-20} eV$ according to our most conservative estimate), and that spin measurements for the largest known supermassive black holes could further lower this bound to $mv\lt 10^{-22} eV$. Our analysis relies on a novel framework to study perturbations of rotating Kerr black holes in the slow-rotation regime, that we developed up to second order in rotation, and that can be extended to other spacetime metrics and other theories.

Marko Stosic, Instituto de Sistemas e Robótica
Knots and HOMFLY I

In these two talks, I'll give a list of structural properties of colored HOMFLY homology that categorifies colored HOMFLY polynomial. The main ingredients are the colored differentials that relate homological invariants of knots colored by different representations. The differentials are predicted by the physics insights that include BPS states counting, Landau-Ginzburg theories. They give a very rigid structure on colored HOMFLY homology theories and also relate them to the super-A-polynomial that categorifies A-polynomial of a knot.

Marko Stosic, Instituto de Sistemas e Robótica
Knots and HOMFLY II

In these two talks, I'll give a list of structural properties of colored HOMFLY homology that categorifies colored HOMFLY polynomial. The main ingredients are the colored differentials that relate homological invariants of knots colored by different representations. The differentials are predicted by the physics insights that include BPS states counting, Landau-Ginzburg theories. They give a very rigid structure on colored HOMFLY homology theories and also relate them to the super-A-polynomial that categorifies A-polynomial of a knot.

Sebastian Guttenberg, CAMGSD
The Quantum Siegel Algebra

The Siegel Algebra is the classical gauge constraint algebra of the Green Schwarz Superstring and as such an extension of the classical Virasoro algebra. It is a long standing problem to obtain an anomaly free quantum version of it. This problem was kind of forgotten when Berkovits introduced his pure spinor superstring, which now commonly replaces the Green Schwarz string at quantum level. However, ghost-extended Siegel operators reappear in the pure spinor formalism in the so-called b-ghost chain. In this talk I will first present the Siegel algebra in terms of operator product expansions (OPE), together with the anomalies that appear at quantum level in absence of ghosts. Then I will show for which ghost-extension of the Siegel operators we found a cancellation of all those anomalies that we could check so far. The resulting Quantum Siegel Algebra contains more operators, but also interesting structures like the b-ghost chain. It should give a whole new understanding of the gauge constraints in the pure spinor formalism and its relation to the Green Schwarz string. If there is time, I might also comment on the Mathematica code that was used to do the OPE calculations. The subject of the talk is work in progress with Ricardo Schiappa.

Daniel Waldram, Imperial College London
Generalised geometry and supergravity

Supergravity is an extension of Einstein gravity that appears as the low-energy description of string theory. We show how “generalised geometry”, a class of extensions of conventional differential geometry first introduced by Hitchin, gives a natural way of formulating supergravity theories. This formulation unifies the bosonic fields and symmetries and has a natural action of $O(d,d)$ or the exceptional groups $E_d$ in $d$-dimensions. By introducing the analogue of the Levi-Civita connection we find that full set of bosonic equations of motion reduce to simply the vanishing of the generalised Ricci tensor. We show that the connection also encodes the supersymmetry variations and fermionic equations of motion. This formalism gives natural extensions of complex, symplectic and other integrable structures, with implications for describing supersymmetric string theory backgrounds.

Jorge Rocha, CENTRA
Inverse Scattering Construction of Black Objects 1

In this series of two talks I will review the construction of exact black hole solutions in higher-dimensional gravitational theories. The first talk will be concerned with the classification of stationary and axisymmetric higher-dimensional black hole spacetimes. This will be based on the very useful concept of rod structure.

Jorge Rocha, CENTRA
Inverse Scattering Construction of Black Objects 2

In this series of two talks I will review the construction of exact black hole solutions in higher-dimensional gravitational theories. The second talk will focus on the Inverse Scattering Method as an efficient tool to generate higher dimensional black objects in vacuum gravity. I will end by mentioning the state-of-the-art in the construction of 5D black rings in theories of gravity coupled to Maxwell and dilation fields.

Jai Grover, University of Aveiro
Enhanced AdS Horizons

We shall identify the conditions under which there is near-horizon supersymmetry enhancement for supersymmetric black hole solutions to minimal five dimensional gauged supergravity. As all known black holes of the gauged theory exhibit supersymmetry enhancement from 1/4 to 1/2 in the near horizon limit, it is natural to investigate if this is generic. A further motivation is that one can demonstrate, assuming supersymmetry enhancement, the existence of two commuting rotational isometries of the full solution. And it is known that under this latter condition there are no asymptotically AdS supersymmetric black ring solutions with regular horizons.

Nguyen Tien Zung, Institut de Mathématiques de Toulouse
Torus actions in normalization problems of dynamical systems

All dynamical system, including non-hamiltonian and non-integrable ones, admits a natural intrinsic commutative symmetry group (torus action) which preserves not only the system but also any tensor field which is invariant with respect to the system. I will discuss the role played by these torus actions in the normalization problems, including action-angle variables, Poincare-Birkhoff normalization, and renormalization group method. Joint Strings-Geolis seminar.