No abstract

We explain how D-branes on group manifolds are stabilized against shrinking by quantized worldvolume U(1) fluxes. Starting from the Born-Infeld action in the case of the SU(2) group manifold we derive the masses, multiplicities and spectrum of small fluctuations of these branes, and show that they agree exactly with the predictions of Conformal Field Theory, to all orders in the α ′ expansion. We discuss the generalization to other groups and comment on an apparent paradox: why are the 'RR charges' of these branes not quantized?

We discuss the equivalence between Type I, Type II and Heterotic N = 2 superstring theories in four dimensions. We study the effective field theory of Type I models obtained by orientifold reductions of Type IIB compactifications on K 3 × T 2 . We show that the perturbative prepotential is determined by the one-loop corrections to the Planck mass and is associated to an index. As is the case for threshold corrections to gauge couplings, this renormalization is entirely due to N = 2 BPS states that originate from D = 6 massless string modes. We apply our result to the so-called S-T -U model which admits simultaneous Type II and Heterotic descriptions, and show that all three prepotentials agree in the appropriate limits as expected from the superstring triality conjecture.

We study D-branes of the SL(2, R) WZW model and of its discrete orbifolds. Gluing the currents by group automorphisms leads to three types of D-branes: two-dimensional hyperbolic planes (H 2 ), de Sitter branes (dS 2 ), or anti-de Sitter branes (AdS 2 ). We explain that the dS 2 branes are unphysical, because the electric field on their world-volume is supercritical. By combining SL(2, R) and SU(2), we exhibit a class of supersymmetric AdS 2 × S 2 three-brane world-volumes, and consider their possible embeddings in the near-horizon region of stringy black holes. We point out the intriguing difference between the induced and the effective geometries of these D-branes, and speculate on its possible significance. Dedicated to the memory of Lochlainn O'Raifeartaigh, who among his many important contributions was also the first to study string theory on SL(2, R). 7644. * See also [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] for related works.to be a non-commutative field theory on the fuzzy two-sphere [54]. Within the semiclassical analysis, the result follows at least qualitatively from the observation that the antisymmetric-tensor flux through the two-sphere can be made much larger than the induced metric † . One has thus a curved-space analog of the decoupling limit considered in [55,56,57]. For the AdS 2 D-branes of SL(2, R), which we will exhibit in the present work, the situation turns out again to be subtler. The AdS 2 branes are the world-volumes of D-strings carrying an electric field that can, if desired, be tuned to its critical limit. This provides a curved-space analog of the non-commutative open-string theories, whose existence was conjectured in references [58,59].The plan of this paper is as follows: in Section 2 we will consider symmetric gluing conditions for SL(2, R), and discuss the geometry of the corresponding D-branes. These were analysed previously by Sonia Stanciu [44], whose results we will extend in several ways. We will show, in particular, that in addition to regular conjugacy classes, which are two-dimensional hyperbolic (H 2 ) or de Sitter (dS 2 ) spaces, there exist twined conjugacy classes with two-dimensional anti-de Sitter geometry (AdS 2 ). These are the only "physically admissible" world-volumes, as we will explain in the next two sections. Specifically, in Section 3 we will see that the dS 2 world-volumes describe, in cylindrical coordinates, circular D-strings which reach the boundary of AdS 3 in a finite time. We will explain why this is impossible, and identify the "pathology" as a supercritical world-volume electric field. We will also exhibit oscillating trajectories, which break the diagonal SL(2, R) invariance and provide interesting examples of non-symmetric boundary conditions in WZW models. In Section 4 we will analyse similarly the AdS 2 world-volumes, which correspond to static (1, q) strings stretching across antipodal points on the AdS 3 boundary. We will show that these AdS 2 world-volumes are the only static solutions of the Dirac-Born-Infel...

We compute threshold effects to gauge couplings in four-dimensional Z N orientifold models of type I strings with N = 2 and N = 1 supersymmetry, and study their dependence on the geometric moduli. We also compute the tree-level (disk) couplings of the open sector gauge fields to the twisted closed string moduli of the orbifold in various models and study their effects and that of the one-loop threshold corrections on gauge coupling unification. We interpret the results from the (supergravity) effective theory point of view and comment on the conjectured heterotic-type I duality.-2-6 This amounts to different ultraviolet cutoffs in the direct channel for the annulus and the Möbius diagrams, see the relations (2.12).