Week 05.10.2009 – 11.10.2009

I will review the gauge/string correspondence, with particular emphasis on recent exact results based on integrable techniques.

I talk about finite corrections to the large spin asymptotics of N=4 SYM twist operators. These corrections are an all-loop result, not affected by wrapping effects, and agree, after determining the strong coupling expansion, with string theory predictions. The finite order corrections enter the sub-leading poles of the logarithm of multi loop gluon scattering amplitudes and describes the difference between the former and the expectation value of certain Wilson lines. For the complete sub-leading pole structure however a second function is needed. A few comments on the quest for a search of a possible description of the latter in terms of local operators will be given.

In this talk, I will discuss a new family of supersymmetric Wilson loop operators in N=4 SYM. These operators can be defined for any loop on a three-sphere in space-time and generically preserve two super-conformal charges. On the string side, via AdS/CFT duality, these loops map to surfaces which are 'pseudo-holomorphic' with respect to a novel almost-complex structure defined on a suitable subspace of AdS5xS5. Of particular interest is the subclass of loops lying on a two-sphere in space-time whose expectation value is conjectured to be computed exactly in terms of the analogous observables in bosonic 2d Yang-Mills on S2. Several evidences for this conjecture, both on the gauge theory and on the string theory side will be discussed.

Over the last years, gauge/string duality has been extended to include gauge theories with an arbitrary number of flavors. We study the flavoring procedure in the light of calibrated geometry and discuss the special case of a type IIA dual of N=1 super Yang-Mills with flavors. Relating our results to the standard type IIA/M-theory duality, we find that the usual oxidation formulas cannot accommodate for the additional flavor branes. We address and solve this issue by considering M-theory with torsion, which allows us to construct source-modified equations of motion for eleven-dimensional supergravity.

Solvmanifolds, in particular nilmanifolds, commonly known as twisted tori, provide several examples of internal manifolds in flux compactifications towards de Sitter, Minkowski or Anti de Sitter. The relation between these manifolds and the six-dimensional torus, and the string vacua obtained on them, are the main interests of this talk. We will first present some properties of these manifolds. We will give a generic construction of their Maurer-Cartan forms out of the six-dimensional torus, via a transformation called the twist. We will then describe several Minkowski flux backgrounds of type II supergravity obtained on these manifolds. Thanks to the generalized complex geometry approach, we will show that one can obtain those solutions from solutions on the torus, via the twist transformation. The latter then acts as a solution generating technique, being able to relate backgrounds which are not T-duals. Finally, we will apply this twist transformation technique to relate Kahler/non-Kahler solutions of the heterotic string. This talk is based on a work with Enrico Goi, Ruben Minasian and Michela Petrini.