Heterotic/Heterotic Duality in D=6,4

Abstract

We consider $E_8\times E_8$ heterotic compactifications on $K3$ and $K3\times T^2$. The idea of heterotic/heterotic duality in $D=6$ has difficulties for generic compactifications since for large dilaton values some gauge groups acquire negative kinetic terms. Recently Duff, Minasian and Witten (DMW) suggested a solution to this problem which only works if the compactification is performed assuming the presence of symmetric gauge embeddings on both $E_8$'s. We consider an alternative in which asymmetric embeddings are possible and the wrong sign of kinetic terms for large dilaton value is a signal of spontaneous symmetry breaking. Upon further toroidal compactification to $D=4$, we find that the duals in the DMW case correspond to $N=2$ models in which the $\beta$-function of the different group factors verify ${\beta }_{\alpha }=12$, whereas the asymmetric solutions that we propose have ${\beta }_{\alpha }=24$. We check the consistency of these dualities by studying the different large $T,S$ limits of the gauge kinetic function. Dual $N=1$, $D=4$ models can also be obtained by the operation of appropriate freely acting twists, as shown in specific examples.

15 pages, latex

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• 6D supergravity without tensor multiplets
• New Higgs Transitions between Dual N=2 String Models
• Holomorphic Couplings in String Theory
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• Multiple Realisations of N=1 Vacua in Six Dimensions
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• Non-perturbative triality in heterotic and type II N=2 strings
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• Lectures on Heterotic-Type I Duality
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• String Vacua with N=2 Supersymmetry in Four Dimensions
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• An Entropy-Weighted Sum over Non-Perturbative Vacua
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• Matrix Description of Heterotic Theory on K3
• Charged Black Holes with Scalar Hair