We construct all 11-dimensional, three-charge BPS solutions that preserve a fixed, standard set of supersymmetries. Our solutions include all BPS three-charge rotating black holes, black rings, supertubes, as well as arbitrary superpositions of these objects. We find very large families of black rings and supertubes with profiles that follow arbitrary closed curves in the spatial $\mathbb{R}^4$ transverse to the branes. The black rings copiously violate black-hole uniqueness. The supertube solutions are completely regular and generically have small curvature. They also have the same asymptotics as the three-charge black hole; so they might be mapped to microstates of the D1–D5–p system and used to explain the entropy of this black hole.

We discuss a classical integrability in the type IIB string theory on the $\mathrm{AdS}_5\times \mathrm{S}^5$ background. By using the Roiban-Siegel formulation of the superstring on the $\mathrm{AdS}_5\times \mathrm{S}^5$, we carefully treat the Wess-Zumino term and the constraint conditions intrinsic to the supersymmetric case and construct explicitly non-local charges for a hidden infinite-dimensional symmetry. The existence of the symmetry is shown by Bena-Polchinski-Roiban. Then the super Yangian algebra is calculated. We also show the Serre relation ensuring the structure of the Hopf algebra. In addition, the classical integrability is discussed by constructing the Lax pair and the transfer matrix.

In this paper we study the matter form of the conformal and super-conformal ghosts action. That is, the ghost fields will be expressed in terms of some scalar and spinor fields. Thus, we obtain a two-dimensional covariant action in the matter form, i.e., $S_g$. The Poincaré-like symmetries and various supersymmetries of this covariant action are analyzed. The signatures 10$+$2 and 11$+$3 for the total target space of the superstring theory also will be discussed.

We reexamine the effects of T-duality on the global properties for principal circle bundles in the context of a dimensionally reduced Gysin sequence. We then construct a Gysin sequence for principal torus bundles and examine the consequences. In particular, we argue that the T-dual of a principal torus bundle with nontrivial H-flux is, in general, a continuous field of noncommutative, nonassociative tori.

We use the exact instanton expansion to illustrate various string characteristics of non-commutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours. The decompactification limit of non-commutative torus instantons is shown to map in a very precise way, at both the classical and quantum levels, onto fluxon solutions on the non-commutative plane. The weak-coupling singularities of the usual Gross–Taylor string partition function for QCD on the torus are studied in the instanton representation and its double-scaling limit, appropriate for the mapping onto non-commutative gauge theory, is shown to be a generating function for the volumes of the principal moduli spaces of holomorphic differentials. The non-commutative deformation of this moduli space geometry is described and appropriate open string interpretations are proposed in terms of the fluxon expansion.