Lectures on Heterotic-Type I Duality

We present a review of heterotic-type I string duality. In particular, we discuss the effective field theory of six- and four-dimensional compactifications with N>1 supersymmetries. We then describe various duality tests by comparing gauge couplings, N=2 prepotentials, as well as higher-derivative F-terms. Based on invited lectures delivered at: 33rd Karpacz Winter School of Theoretical Physics ``Duality, Strings and Fields,'' Przesieka, Poland, 13 - 22 February 1997; Trieste Conference on Duality Symmetries in String Theory, Trieste, Italy, 1 - 4 April 1997; Cargese Summer School ``Strings, Branes and Dualities,'' Cargese, France, 26 May - 14 June 1997.Comment: 14 pages, LaTeX, espcrc2.st

Duality of N=2 Heterotic -- Type I Compactifications in Four Dimensions

We discuss type I -- heterotic duality in four-dimensional models obtained as a Coulomb phase of the six-dimensional U(16) orientifold model compactified on T^2 with arbitrary SU(16) Wilson lines. We show that Kahler potentials, gauge threshold corrections and the infinite tower of higher derivative F-terms agree in the limit that corresponds to weak coupling, large T^2 heterotic compactifications. On the type I side, all these quantities are completely determined by the spectrum of N=2 BPS states that originate from D=6 massless superstring modes.Comment: 22 pages, LaTeX; typos corrected and references adde

Non Perturbative Check of N=2, D=4 Heterotic/Type II Duality

We review here some of the checks of string-string duality between N=2, D=4 Heterotic and Type II models. The heterotic low energy field theory is reproduced on the type II side. It is also shown to be a generalization in the string context of the rigid $N=2$ Yang-Mills theory of Seiberg and Witten which is exactly known. The non perturbative information of this rigid theory is then recovered on the type II side. This talk is based on a work done in collaboration with I. Antoniadis.Comment: Contribution to the proceedings of the Spring School and Workshop on String Theory, Gauge Theory and Quantum Gravity, I.C.T.P., Trieste, Italy, March 18-29. latex2e, uses espcrc2.st

Inflation from Supergravity with Gauged R-symmetry in de Sitter Vacuum

We study the cosmology of a recent model of supersymmetry breaking, in the presence of a tuneable positive cosmological constant, based on a gauged shift symmetry of a string modulus that can be identified with the string dilaton. The minimal spectrum of the `hidden' supersymmetry breaking sector consists then of a vector multiplet that gauges the shift symmetry of the dilaton multiplet and when coupled to the MSSM leads to a distinct low energy phenomenology depending on one parameter. Here we study the question if this model can also lead to inflation by identifying the dilaton with the inflaton. We find that this is possible if the K\"ahler potential is modified by a term that has the form of NS5-brane instantons, leading to an appropriate inflationary plateau around the maximum of the scalar potential, depending on two extra parameters. This model is consistent with present cosmological observations without modifying the low energy particle phenomenology associated to the minimum of the scalar potential.Comment: 19 pages, 5 figures, References adde

Making Ends Meet: String Unification and Low-Energy Data

A long-standing problem in string phenomenology has been the fact that the string unification scale disagrees with the GUT scale obtained by extrapolating low-energy data within the framework of the minimal supersymmetric standard model (MSSM). In this paper we examine several effects that may modify the minimal string predictions and thereby bring string-scale unification into agreement with low-energy data. These include heavy string threshold corrections, non-standard hypercharge normalizations, light SUSY thresholds, intermediate gauge structure, and thresholds arising from extra matter beyond the MSSM. We explicitly evaluate these contributions within a variety of realistic free-fermionic string models, including the flipped SU(5), SO(6) x SO(4), and various SU(3) x SU(2) x U(1) models, and find that most of these sources do not substantially alter the minimal string predictions. Indeed, we find that the only way to reconcile string unification with low-energy data is through certain types of extra matter. Remarkably, however, many of the realistic string models contain precisely this required matter in their low-energy spectra.Comment: 10 pages, standard LaTeX, 1 figure (Encapsulated PostScript), version published in Phys. Rev. Lett. 75 (1995) 264

Exact monodromy group of N=2 heterotic superstring

We describe an N=2 heterotic superstring model of rank-3 which is dual to the type-II string compactified on a Calabi-Yau manifold with Betti numbers b_{1,1}=2 and b_{1,2}=86. We show that the exact duality symmetry found from the type-II realization contains the perturbative duality group of the heterotic model, as well as the exact quantum monodromies of the rigid SU(2) super-Yang-Mills theory. Moreover, it contains a non-perturbative monodromy which is stringy in origin and corresponds roughly to an exchange of the string coupling with the compactification radius

The g-2 of the Muon in Localized Gravity Models

The (g-2) of the muon is well known to be an important model building constraint on theories beyond the Standard Model. In this paper, we examine the contributions to $(g-2)_\mu$ arising in the Randall-Sundrum model of localized gravity for the case where the Standard Model gauge fields and fermions are both in the bulk. Using the current experimental world average measurement for $(g-2)_\mu$, we find that strong constraints can be placed on the mass of the lightest gauge Kaluza-Klein excitation for a narrow part of the allowed range of the assumed universal 5-dimensional fermion mass parameter, $\nu$. However, employing both perturbativity and fine-tuning constraints we find that we can further restrict the allowed range of the parameter $\nu$ to only one fourth of its previous size. The scenario with the SM in the RS bulk is thus tightly constrained, being viable for only a small region of the parameter space.Comment: 16 pages, 2 figs, LaTex, Additional discussion adde

Unification with Enlarged Kaluza-Klein Dimensions

In minimal theories with extra spatial dimensions at scales mu_0 much lower than the conventional GUT scale, unification can give too-large predictions for alpha_3(M_Z) given alpha_1(M_Z) and alpha_2(M_Z) as empirical input. We systematically study the effects of adding extra states above the compactification scale on running of the gauge couplings and find several simple examples that give unification where all alpha_i(M_Z) are consistent with low-energy data. We study both the supersymmetric and nonsupersymmetric unification.Comment: 18 pages, LaTeX, analysis for the susy case takes into account that extra hypermultiplets come in conjugate pairs, minor changes in text and references, to be published in Phys. Lett.

Unitarity of Compactified Five Dimensional Yang-Mills Theory

Compactified five dimensional Yang-Mills theory results in an effective four-dimensional theory with a Kaluza-Klein (KK) tower of massive vector bosons. We explicitly demonstrate that the scattering of the massive vector bosons is unitary at tree-level for low energies, and analyze the relationship between the unitarity violation scale in the KK theory and the nonrenormalizability scale in the five dimensional gauge theory. In the compactified theory, low-energy unitarity is ensured through an interlacing cancellation among contributions from the relevant KK levels. Such cancellations can be understood using a Kaluza-Klein equivalence theorem which results from the geometric ``Higgs'' mechanism of compactification. In these theories, the unitarity violation is delayed to energy scales higher than the customary limit through the introduction of additional vector bosons rather than Higgs scalars.Comment: 10 pages, 1 eps figure, discussion of deconstruction expanded, version accepted for publication in PL