Compact Calabi-Yau manifolds are a key ingredient for dimensional reduction in string theory. For this, one requires the Ricci-flat metric on these manifolds. Whilst Yau proved this metric exists, no explicit smooth examples are known, essentially as it is very difficult (impossible?) to find them analytically as they have no continuous isometries. Taking a new approach, I will discuss numerical methods to solve the Einstein equation on these manifolds. I will pedagogically describe the construction, and give results, for a particular one parameter family of metrics on K3 (the unique 4-dimensional Calabi-Yau manifold). I will discuss possible applications of these methods, and generalizations to geometries with matter such as those relevant for flux compactifications. There will be some nice pictures.

This seminar reviews some of the global algebraic and geometric structure present in T-duality. Bouwknegt, Evslin and Mathai have given a geometric procedure for handling T-duality for certain non-trivial principal torus bundles. Subsequent work by Mathai and Rosenberg showed that sometimes when there is no geometric T-dual there may be a non-commutative torus bundle playing the same role. This exploited a very similar duality for C-star-algebras known for a couple of decades. This talk will review those developments and their recent extension in collaboration with Bouwknegt and Mathai to more general situations in which the algebraic structure becomes non-associative.

String Theory and Geometry Seminar

After a general overview, the construction of D-brane boundary states in the pure spinor superstring will be discussed.

I review general features of AdS/CFT models with dynamical quarks, with particular emphasis on chiral dynamics. I also show how these models incorporate the nontrivial interplay between the solution of the U(1) problem in QCD and the 1/N expansion.

INSTITUTE FOR MATHEMATICAL SCIENCES LAUNCH WEEK

INSTITUTE FOR MATHEMATICAL SCIENCES LAUNCH WEEK

We discuss quantum fluctuations of a class of rotating strings in AdS5xS5. In particular, we develop a systematic method to compute the one-loop sigma-model effective actions in closed forms for large angular momenta. As examples, we explicitly evaluate the leading terms for the constant radii strings in the SO(6) sector with two equal angular momenta, the SU(2) sector, and the SL(2) sector. We also obtain the leading quantum corrections to the space-time energy for these sectors.

We describe duality cascades and their infrared behavior for gauge theories on D3-branes at singularities in the presence of fractional branes. From the gauge field theory viewpoint, we show that D3-branes probing the infrared theory have a quantum deformed moduli space, given by a complex deformation of the initial geometry to a simpler one. Thus the gauge theory strong infrared dynamics smoothes out the naked singularities of the recently constructed dual supergravity warped throat solutions with 3-form fluxes. This behaviour thus generalizes the Klebanov-Strassler deformation of the conifold. We describe several explicit examples, including models with several scales of strong gauge dynamics, whose dual should correspond to throats with several radial regions with different exponential warp factors. These rich throat geometries have interesting applications in compactification and model building.

We will argue that the cigar conformal field theory SL(2,R)/U(1) is a prime example of a non-rational conformal field theory and we exhibit some of its characteristic features that might generalize to other non-rational conformal field theories. We discuss how this particular non-rational conformal field theory (with or without boundary) arises in string theory backgrounds with NS5-branes, and how the technical advances reached in the conformal field theory can illuminate aspects of holography in these backgrounds.

I will discuss the philosophy of the Euclidean field theory approach to black hole thermodynamics. I will then illustrate some of the difficulties presented by rotating black holes in AdS. Next, I will relate these results to the AdS-CFT correspondence. Finally, I will discuss the question of black rings, and make some heterodox comments on the difficulties that they pose for the Euclidean formulation.

I will review a recently proposed method for solving the Killing spinor equations in arbitrary dimensions. The efficiency of the method will be illustrated by recent progress on the classification of the supersymmetric solutions of 11D and IIB supergravity.

I will discuss the relation between bulk and boundary for the smooth 'bubble of nothing' solution in AdS, and for the locally AdS black hole. I will explain the relation between horizons and thermodynamics in bulk and boundary, and discuss vacuum ambiguities.

I want to study Q-Fano 3-folds from the point of view of mirror symmetry. In this talk I make some remarks and try some questions.

The standard prescription for calculating a Wilson loop in the AdS/CFT correspondence is by a string world-sheet ending along the loop at the boundary of AdS. For a multiply wrapped Wilson loop this leads to many coincident strings, which may interact among themselves. In such cases a better description of the system is in terms of a D3-brane carrying electric flux. We find such solutions for the single straight line and the circular loop. The action agrees with the string calculation at small coupling and in addition captures all the higher genus corrections at leading order in alpha'. The resulting expression is in remarkable agreement with that found from a zero dimensional Gaussian matrix model.