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Register a new userLectures on Heterotic-Type I Duality
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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.
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We compute the partition function for the exotic instanton system corresponding to D-instantons on D7 branes in Type I theory. We exploit the BRST structure of the moduli action and its deformation by RR background to fully localize the integration. The resulting prepotential describes non-perturbative corrections to the quartic couplings of the gauge field F living on the D7s. The results match perfectly those obtained in the dual heterotic theory from a protected 1-loop computation, thus providing a non-trivial test of the duality itself.
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.
We show how the brane wrapping rules, recently discovered in closed oriented string theories compactified on tori, are extended to the case of the Type IIA string compactified on K3. To this aim, a crucial role is played by the duality between this theory and the Heterotic string compactified on a four-dimensional torus T^4. We first show how the wrapping rules are applied to the T^4/Z_N orbifold limits of K3 by relating the D0 branes, obtained as D2 branes wrapping two-cycles, to the perturbative BPS states of the Heterotic theory on T^4. The wrapping rules are then extended to the solitonic branes of the Type IIA string, finding agreement with the analogous Heterotic states. Finally, the geometric Type IIA orbifolds are mapped, via T-duality, to non-geometric Type IIB orbifolds, where the wrapping rules are also at work and consistent with string dualities.
The moduli space of toroidal type I vacua, which are consistent at the non-perturbative level, consists of independent branches characterized by the number (0, 16 or 32) of rigid branes sitting on top of orientifold planes. This structure persists also when supersymmetry is spontaneously broken a la Scherk-Schwarz. We show that all the components of the moduli space in dimension $Dge 5$ indeed admit heterotic dual components, by explicitly constructing heterotic-type I dual pairs with the rank of the gauge group reduced by 0, 8 or 16 units. In the presence of spontaneous breaking of supersymmetry, the dual pairs we consider are also free of tachyonic instabilities at the one-loop level, provided the scale of supersymmetry breaking is lower than the string scale.
The three generation heterotic-string models in the free fermionic formulation are among the most realistic string vacua constructed to date, which motivated their detailed investigation. The classification of free fermion heterotic string vacua has revealed a duality under the exchange of spinor and vector representations of the SO(10) GUT symmetry over the space of models. We demonstrate the existence of the spinor-vector duality using orbifold techniques, and elaborate on the relation of these vacua to free fermionic models.
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