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.

D-instantons are Euclidean (-1)-brane solutions of type IIB supergravity, which have been used to compute non-perturbative corrections to the effective action of type IIB string theory. I will discuss the most general non-extremal, non-supersymmetric generalization to the D-instanton. By repeating the calculations for arbitrary dimensions and dilaton coupling we will see that these solutions can be viewed as wormholes of non-extremal Reissner-Nordstroem black holes in one higher dimension. I will also discuss the role of D-instantons in the context of AdS/CFT and make a conjecture about the CFT counterpart of these non-extremal solutions.

Massive (perturbative) string states are interesting in many respects (cosmology, black hole Physics, production at accelerators). We review the research done in order to find the perturbative massive superstring states with very long lifetime, the characteristics of their decay, the emission spectrum, both in fully extended space-time and in the case of toroidal compactifications. The main result is the identification of a particular state with very long lifetime decaying only by gravitational emission and with thermal-like spectrum.

I will discuss the newly discovered Y(p,q) quiver gauge theories, which are dual to Type IIB string theory on AdS5 x Y(p,q). The metrics on the five-dimensional Y(p,q) manifolds are explicitly known, thus opening up exciting possibilities. Special emphasis will be placed on the toric phases of these theories and their Seiberg duality structure.

We consider the heterotic string on certain six-dimensional half-flat manifolds which arise in the context of mirror symmetry. The four-dimensional N=1 effective theory is derived including the superpotential induced by the intrinsic torsion and NS NS flux. From the calculation of the gravitino mass term, we also obtain a general Gukov type formula valid for all heterotic compactifications on manifolds with SU(3) structure. The results are used to study heterotic AdS4 vacua which arise from the flux superpotential combined with gaugino condensation.

I will give an introduction to the novel method of calculating scattering amplitudes in gauge theory with twistor-space string theory inspired rules. I will show how the method works in simple cases and discuss recent new results for the amplitudes obtained at tree and loop level. I'll discuss some known puzzles, the ways to resolve them, open questions and future directions, including issues in string theory, quantum field theory and phenomenology.

This talk is part of the joint Triangular Seminars.

Using the example of WZW D-branes, I will explain how loop operators, corresponding to bulk conformal defects, generate new consistent D-branes from old ones. I will comment on possible extensions to more general geometries.

We will generalize the concept of partial and complete observables, intruduced by Rovelli, to constrained systems with an arbitrary number of (first class) constraints and to canonical field theories. Different methods to calculate complete observables (aka Dirac observables) will be presented and applied to examples, moreover their algebraic properties will be considered. Furthermore we will investigate whether it is possible to calculate complete observables in stages. In the case of gravity this will answer the question , whether it is possible to calculate the complete observable with respect to the Hamiltonian constraints, starting from 3-diffeomorphism invariant partial observables.

In the supergravity approximation of the AdS/CFT correspondence correlation fucntions of the strongly coupled gauge theory can be computed by evaluating the on-shell supergravity action with arbitrary Dirichlet boundary conditions for the various fields. It is well known, however, that the on-shell action on the conformal boundary of AdS diverges due to the infinite volume of the bulk. Holographic Renormalization is a method for systematically constructing covariant counter terms which remove the divergences of the on-shell supergravity action for any asymptotically AdS space and it provides an algorithm for calculating renormalized correlation functions of the strongly coupled gauge theory. I will review the main steps involved in this algorithm and present a recently developed Hamiltonian version of the method where the AdS radius plays the role of time in the Hamiltonian formalism. I will then apply this method to calculate correlation functions in the field theory duals of various Poincare and AdS-sliced domain wall solutions of five dimensional gauged supergravity, including the recently discovered Janus background.