Seminário de Teoria de Cordas  

Magnetic monopoles develop "abelian" singularities in rather general situations. At first, this was seen as a somewhat embarrassing fact by physicists, yet singular monopoles have become important in recent applications of gauge theory to geometry. In this talk, I will review singular monopoles in euclidean space, and explain how they are described by a complex curve with a signed intersection divisor. I will also discuss how these data can be calculated in the case of "nonabelian" charge two, as well as some features of their behaviour under deformations of the singularity locus.

Berkovits' pure spinor string (type II) will be discussed in a general superspace background. The derivation of the supergravity constraints from classical BRST invariance will carefully be reviewed and new aspects added. Then it will be sketched how to extract the supersymmetry transformations of the physical fields.

In this talk I present a new formalism for computing unambiguously open and closed topological string amplitudes. The formalism is based on a recursive method for computing invariants of algebraic curves recently proposed by Eynard and Orantin. The resulting amplitudes are non-perturbative in both the closed and the open moduli. The computational efficiency of this formalism can be dramatically increased by rewriting the amplitudes in a form that makes their transformation properties under the modular group manifest. As an application of this method I will illustrate how to compute open Gromov-Witten invariants for the $C^3/Z_3$ orbifold.

I shall present the construction of a certain geometric representation of KO-homology, the homological theory associated with KO-theory, inspired by the work of Paul Baum and Ronald Douglas on K-homology. I'll also discuss its application to the construction and classification of D-brane charges in the absence of a background B-field.

In this talk I will describe how supersymmetric gauged sigma-models and mirror symmetry can be used to compute the quantum equivariant cohomology ring of toric manifolds in a simple way.

The AdS/CFT duality [1] is a conjecture relating string theory in some curved background and a certain four dimensional gauge theory which can be regarded as a toy model for QCD. The perturbative (easy) regime of one of the theories is dual to the strongly coupled (hard) regime of the dual theory. Thus, we might wonder whether it could be possible to use this conjecture as an inspiration/guide to solve each of the theories exactly? A priori this might seem a superhuman task but, since (four years ago) an integrable structure behind these theories was found [2], the distance towards this goal is being reduced at an amazing pace. I will try to explain the Bethe ansatz formalism (appearing naturally from the Gauge theory side [3]) and the algebraic curve construction (emerging in the string theory side [4]) and I will explain the motivation behind the various conjectures [5] which seem to connect these two formalisms. In this way I will try to transmit where we are (that is, what is proven and what is conjectured) and what are the most likely advances in the short term (that is, in which direction is this science moving).

The following list of references is obviously not extensive:

1. The Large $N$ limit of superconformal field theories and supergravity. Juan M. Maldacena hep-th/9711200 Gauge theory correlators from noncritical string theory. S.S. Gubser, Igor R. Klebanov, Alexander M. Polyakov hep-th/9802109 Anti-de Sitter space and holography. Edward Witten hep-th/9802150.
2. The Bethe ansatz for $N=4$ superYang-Mills. J.A. Minahan, K. Zarembo hep-th/0212208. Hidden symmetries of the $\mathrm{AdS}(5)\times S^5$ superstring. Iosif Bena, Joseph Polchinski, Radu Roiban hep-th/0305116
3. The Bethe ansatz for $N=4$ superYang-Mills. J.A. Minahan, K. Zarembo hep-th/0212208 The Dilatation operator of $N=4$ super Yang-Mills theory and integrability. Niklas Beisert hep-th/0407277.
4. Classical/quantum integrability in AdS/CFT. V.A. Kazakov, A. Marshakov, J.A. Minahan, K. Zarembo hep-th/0402207. The Algebraic curve of classical superstrings on $\mathrm{AdS}(5)\times S^5$. N. Beisert, V.A. Kazakov, K. Sakai, K. Zarembo hep-th/0502226.
5. Transcendentality and Crossing. Niklas Beisert, Burkhard Eden, Matthias Staudacher hep-th/0610251 A Crossing-symmetric phase for $\mathrm{AdS}(5)\times S^5$ strings. Niklas Beisert, Rafael Hernandez, Esperanza Lopez hep-th/0609044

The AdS/CFT duality [1] is a conjecture relating string theory in some curved background and a certain four dimensional gauge theory which can be regarded as a toy model for QCD. The perturbative (easy) regime of one of the theories is dual to the strongly coupled (hard) regime of the dual theory. Thus, we might wonder whether it could be possible to use this conjecture as an inspiration/guide to solve each of the theories exactly? A priori this might seem a superhuman task but, since (four years ago) an integrable structure behind these theories was found [2], the distance towards this goal is being reduced at an amazing pace. I will try to explain the Bethe ansatz formalism (appearing naturally from the Gauge theory side [3]) and the algebraic curve construction (emerging in the string theory side [4]) and I will explain the motivation behind the various conjectures [5] which seem to connect these two formalisms. In this way I will try to transmit where we are (that is, what is proven and what is conjectured) and what are the most likely advances in the short term (that is, in which direction is this science moving).

The following list of references is obviously not extensive:

1. The Large $N$ limit of superconformal field theories and supergravity. Juan M. Maldacena hep-th/9711200 Gauge theory correlators from noncritical string theory. S.S. Gubser, Igor R. Klebanov, Alexander M. Polyakov hep-th/9802109 Anti-de Sitter space and holography. Edward Witten hep-th/9802150.
2. The Bethe ansatz for $N=4$ superYang-Mills. J.A. Minahan, K. Zarembo hep-th/0212208. Hidden symmetries of the $\mathrm{AdS}(5)\times S^5$ superstring. Iosif Bena, Joseph Polchinski, Radu Roiban hep-th/0305116
3. The Bethe ansatz for $N=4$ superYang-Mills. J.A. Minahan, K. Zarembo hep-th/0212208 The Dilatation operator of $N=4$ super Yang-Mills theory and integrability. Niklas Beisert hep-th/0407277.
4. Classical/quantum integrability in AdS/CFT. V.A. Kazakov, A. Marshakov, J.A. Minahan, K. Zarembo hep-th/0402207. The Algebraic curve of classical superstrings on $\mathrm{AdS}(5)\times S^5$. N. Beisert, V.A. Kazakov, K. Sakai, K. Zarembo hep-th/0502226.
5. Transcendentality and Crossing. Niklas Beisert, Burkhard Eden, Matthias Staudacher hep-th/0610251 A Crossing-symmetric phase for $\mathrm{AdS}(5)\times S^5$ strings. Niklas Beisert, Rafael Hernandez, Esperanza Lopez hep-th/0609044

We perform a first principles semi-classical computation of the one-loop corrections to the dispersion relation and $S$-matrix of giant magnons in $\mathrm{Ad}{S}^5\times S^5$ string theory. The results agree exactly with expectations based on the strong coupling expansion of the exact Asymptotic Bethe Ansatz equations. In particular we reproduce the Hernandez-Lopez term in the dressing phase.

We perform a first principles semi-classical computation of the one-loop corrections to the dispersion relation and $S$-matrix of giant magnons in $\mathrm{Ad}{S}^5\times S^5$ string theory. The results agree exactly with expectations based on the strong coupling expansion of the exact Asymptotic Bethe Ansatz equations. In particular we reproduce the Hernandez-Lopez term in the dressing phase.

• Heng-Yu Chen, Nick Dorey, Rui F. Lima Matos, Quantum Scattering of Giant Magnons, arXiv:0707.0668 [hep/th]

This will be a general colloquium for physicists and mathematicians who are not specialists in String Theory.

The main results on anholonomic noncommutative and Finsler geometry in string theory are outlined. The relation of anholonomic frames and nonlinear connections to M-theory and possible noncommutative versions of locally anisotropic supergravity and D-branes are discussed. There are analyzed new classes of exact solutions with noncommutative local anisotropy describing anholonomically deformed black holes (black ellipsoids) in string gravity, embedded Finsler-string two dimensional structures, solitonically moving black holes in extra dimensions and wormholes with noncommutativity and anisotropy induced from string theory.