Perturbative and Non-Perturbative Partial Supersymmetry Breaking; N=4 -> N=2 -> N=1

We show the existence of a supersymmetry breaking mechanism in string theory, where N=4 supersymmetry is broken spontaneously to N=2 and N=1 with moduli dependent gravitino masses. The spectrum of the spontaneously broken theory with lower supersymmetry is in one-to-one correspondence with the spectrum of the heterotic N=4 string. The mass splitting of the N=4 spectrum depends on the compactification moduli as well as the three R-symmetry charges. We also show that, in string theory, chiral theories can be obtained after spontaneous breaking of extended supersymmetry. This was impossible at the level of field theory. In the large moduli limit a restoration of the N=4 supersymmetry is obtained. As expected the graviphotons and some of the gauge bosons become massive in N=1 vacua. At some special points of the moduli space some of the N=4 states with non-zero winding numbers and with spin 0 and {1/2} become massless chiral superfields of the unbroken N=1 supersymmetry. Such vaccua have a dual type II description, in which there are magnetically charged states with spin 0 and {1/2} that become massless. The heterotic-type II duality suggests some novel non-perturbative transitions on the type II side. Such transitions do not seem to have a geometric interpretation, since they relate type II vaccua with symmetric worlsheet structure to assymetric ones. The heteroric interpretation of such a transition is an ordinary Higgsing of an SU(2) factor. In the case of N=4 --> N=2, the perturbative N=2 prepotential is determined by the perturbative N=4 BPS states. This observation let us to suggest a method which determines the exact non-perturbative prepotential of the effective N=2 supergravity using the shifted spectrum of the non-perturbative BPS states of the underlying N=4 theory.Comment: 36 pages, Latex. An important part is added. We point out that there are string theory groundstates with spontaneously broken extended supersymmetry and chiral spectru

Gravitational Phenomena from Superstrings in Curved Spacetime

The four-dimensional superstring solutions define at low energy effective supergravity theories. A class of them extends successfully the validity of the standard model up to the string scale (${\cal O}(10^{17})~TeV$). We stress the importance of string corrections which are relevant for low energy (${\cal O}(1)~TeV$) predictions of gauge and Yukawa couplings as well as the spectrum of the supersymmetric particles. A class of exact string solutions are also presented, providing non trivial space-time backgrounds, from which we can draw some lessons concerning the regions of space-time where the notion of the effective field theory prescription make sense. We show that the string gravitational phenomena may induce during the cosmological evolution, transitions from one effective field theory prescription to a different one where the geometrical and topological data, as well as the relevant observable states are drastically different. Talk presented by C. Kounnas in the XXIX Moriond Meeting, M\'eribel, France.Comment: LateX, 11pp., CERN-TH.7332/9

Dynamical Topology Change, Compactification and Waves in a Stringy Early Universe

Exact string solutions are presented, where moduli fields are varying with time. They provide examples where a dynamical change of the topology of space is occurring. Some other solutions give cosmological examples where some dimensions are compactified dynamically or simulate pre-big bang type scenarios. Some lessons are drawn concerning the region of validity of effective theories and how they can be glued together, using stringy information in the region where the geometry and topology are not well defined from the low energy point of view. Other time dependent solutions are presented where a hierarchy of scales is absent. Such solutions have dynamics which is qualitatively different and resemble plane gravitational waves. Talk presented by E. Kiritsis in the 2\`eme Journ\'ee Cosmologie, Observatoire de Paris, 2-4 June 1994.Comment: LaTeX, 28pp. CERN-TH.7328/9

A Large Class of New Gravitational and Axionic Backgrounds for Four-Dimensional Superstrings

A large class of new 4-D superstring vacua with non-trivial/singular geometries, spacetime supersymmetry and other background fields (axion, dilaton) are found. Killing symmetries are generic and are associated with non-trivial dilaton and antisymmetric tensor fields. Duality symmetries preserving N=2 superconformal invariance are employed to generate a large class of explicit metrics for non-compact 4-D Calabi-Yau manifolds with Killing symmetries.Comment: LateX file, 34pp., (v5) Some misprints corrected in sections 3.1, 3.2 as pointed out in the paper of Hori and Kapustin (hep-th/0203147). Some comsetic changes also made in the same section

Solving the Decompactification Problem in String Theory

We investigate heterotic ground states in four dimensions in which N=4 supersymmetry is spontaneously broken to N=2. N=4 supersymmetry is restored at a decompactification limit corresponding to $m_{3/2}\to 0$. We calculate the full moduli dependent threshold corrections and confirm that they are supressed in the decompactification limit $m_{3/2}\to 0$ as expected from the restoration of N=4 supersymmetry. This should be contrasted with the behavior of the standard N=2 groundstates where the coupling blow up linearly with the volume of the decompactifying manifold. This mechanism provides a solution to the decompactification problem for the gauge coupling constants. We also discuss how the mechanism can be implemented in ground states with lower supersymmetry.Comment: 14pp, LaTeX some typos correcte

Five-Brane Configurations without a Strong Coupling Regime

Five-brane distributions with no strong coupling problems and high symmetry are studied. The simplest configuration corresponds to a spherical shell of branes with S^3 geometry and symmetry. The equations of motions with delta-function sources are carefully solved in such backgrounds. Various other brane distributions with sixteen unbroken supercharges are described. They are associated to exact world-sheet superconformal field theories with domain-walls in space-time. We study the equations of gravitational fluctuations, find normalizable modes of bulk 6-d gravitons and confirm the existence of a mass gap. We also study the moduli of the configurations and derive their (normalizable) wave-functions. We use our results to calculate in a controllable fashion using holography, the two-point function of the stress tensor of little string theory in these vacua.Comment: LateX, 32 pages, 4 figures; (v2) A reference adde

On the Heterotic Effective Action at One-Loop, Gauge Couplings and the Gravitational Sector

We present in detail the procedure for calculating the heterotic one-loop effective action. We focus on gravitational and gauge couplings. We show that the two-derivative couplings of the gravitational sector are not renormalized at one loop when the ground state is supersymmetric. Arguments are presented that this non-renormalization theorem persists to all orders in perturbation theory. We also derive the full one-loop correction to the gauge coupling. For a class of $N=2$ ground states, namely those that are obtained by toroidal compactification to four dimensions of generic six-dimensional $N=1$ models, we give an explicit formula for the gauge-group independent thresholds, and show that these are equal within the whole family.Comment: LateX, 17pp. A minor correction mad

F^4 Terms in N=4 String Vacua

We discuss $F_{\mu\nu}^4$ terms in torroidal compactifications of type-I and heterotic SO(32) string theory. We give a simple argument why only short BPS multiplets contribute to these terms at one loop, and verify heterotic-type-I duality to this order.Comment: 10 pages, Latex. A statement about superinvariants was corrected. Minor cosmetic changes were also made. To appear in Proceedings of Trieste Spring School and Workshop, April 199

Poisson-Lie T-duality

A description of dual non-Abelian duality is given, based on the notion of the Drinfeld double. The presentation basically follows the original paper \cite{KS2}, written in collaboration with P. \v Severa, but here the emphasis is put on the algebraic rather than the geometric aspect of the construction and a concrete example of the Borelian double is worked out in detail.Comment: 11 pages, LaTeX, Lecture given at Trieste conference on S-duality and mirror symmetry, June 1995, (signs in Eqs. (10,11) corrected, 1 reference added