This project concerns the study of Lorentz invariant integrablestructures in the sigma model side of the AdS/CFT correspondence. Inparticular, we are interested in the Pohlmeyer reduction ofGreen-Schwarz (GS) superstring sigma models introduced a few years agoby Grigoriev and Tseytlin and by Mikhailov and Schafer-Nameki at theclassical level. The main motivation is to obtain a reformulation withmanifest relativistic invariance and depending only on thephysical/transverse string degrees of freedom. To date, and for theAdS ×Su GS sigma model, there are very compelling results suggestingthe usefulness of the reduced theory as a tool for a possible novelcovariant quantization method of the superstring. In particular, thereduced theory is UV finite up to two loops, exhibits invariance undera kind of rigid N=(8,8) 2D supersymmetry and there is a family ofexact quantum S-matrices interpolating between the S-matrices of theGS superstring and the reduced theory in two different limits. Inother words, there is a bi-parametric quantum group supersymmetryunderlying the non-relativistic magnon S-matrix and the relativisticsoliton S-matrix, suggesting that the GS sigma model and the reducedtheory are Lagrangian descriptions in two corners of a more generalintegrable quantum field theory.The purpose of this research project is to understand and extendprevious results obtained in the soliton theory of the Pohlmeyerreduced GS sigma models in the D-brane language at classical andquantum levels and also to find the precise connection with the GSsuperstring sigma models, as the reduction is well understood only inone sense. This is useful for a novel understanding of the 2D solitontheory in D-brane terms, both in the bosonic and supersymmetric casesrelevant to the reduction of strings and superstrings. One of the mostimportant aspects will be a systematic study of the possibleintegrable Lagrangian deformations of the reduced theory, theirrelation with the quantum group symmetry of the soliton S-matrix andthe role of D-branes. In particular, the mapping of physicallyrelevant quantities from the reduced model to the GS sigma model andthe relation with the scattering of giant magnons and giant gravitons.
News published in Agência FAPESP Newsletter about the scholarship: