The SL(2,Z) duality symmetry of IIB superstring is naturally realized on the D=11 supermembrane restricted to have central charges arising from a nontrivial wrapping. This supermembrane is minimally immersed on the target space (MIM2). The hamiltonian of the MIM2 has a discrete quantum spectrum. It is manifestly invariant under the SL(2,Z) symmetry associated to the conformal symmetry on the base manifold and under a SL(2,Z) symmetry on the moduli of the target space. The mass contribution of the string states on the MIM2 is obtained by freezing the remaining degrees of freedom. It exactly agrees with the perturbative spectrum of the (p,q) IIB and IIA superstring compactified on a circle. We also construct a MIM2 in terms of a dual target space, then a (p,q) set of non-perturbative states associated to the IIA superstring is obtained.
We investigate how SL(2,Z) duality is realized in nonrelativistic type IIB superstring theory, which is a self-contained corner of relativistic string theory. Within this corner, we realize manifestly SL(2,Z)-invariant (p,q)-string actions. The construction of these actions imposes a branching between strings of opposite charges associated with the two-form fields. The branch point is determined by these charges and the axion background field. Both branches must be incorporated in order to realize the full SL(2,Z) group. Besides these string actions, we also construct D-instanton and D3-brane …
Intersection of black hole theory and quantum chromodynamics: the gluon propagator corresponding to linear confinement at large distances and relativistic bound states in the confining SU(N)-Yang-Mills fields
