We discuss basic properties of the Bäcklund transformations for the classical string in AdS space in the context of the null-surface perturbation theory. We explain the relation between the Bäcklund transformations and the energy shift of the dual field theory state. We show that the Bäcklund transformations can be represented as a finite-time evolution generated by a special linear combination of the Pohlmeyer charges. This is a manifestation of the general property of Bäcklund transformations known as spectrality. We also discuss the plane wave limit.

We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity. The unification is based on the symplectic unitary group in Hilbert space and on the spectral action. It yields all the detailed structure of the standard model with several predictions at unification scale. Besides the familiar predictions for the gauge couplings as for GUT theories, it predicts the Higgs scattering parameter and the sum of the squares of Yukawa couplings. From these relations, one can extract predictions at low energy, giving in particular a Higgs mass around 170 GeV and a top mass compatible with present experimental value. The geometric picture that emerges is that space–time is the product of an ordinary spin manifold (for which the theory would deliver Einstein gravity) by a finite noncommutative geometry $F$. The discrete space $F$ is of KO-dimension 6modulo 8 and of metric dimension 0, and accounts for all the intricacies of the standard model with its spontaneous symmetry breaking Higgs sector.

This note is presenting the generating functions which count the BPS operators in the chiral ring of a $\cal N=2$ quiver gauge theory that lives on N D3-branes probing an ALE singularity. The difficulty in this computation arises from the fact that this quiver gauge theory has a moduli space of vacua that splits into many branches — the Higgs, the Coulomb, and mixed branches. As a result, there can be operators which explore those different branches and the counting gets complicated by having to deal with such operators while avoiding over or under counting. The solution to this problem turns out to be very elegant and is presented in this note. Some surprises with “surgery” of generating functions arises.