R-Symmetry and the Topological Twist of N=2 Effective Supergravities of
  Heterotic Strings

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Abstract

We discuss R-symmetries in locally supersymmetric N=2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable R-symmetry exists and can be used to topologically twist the theory: the vector multiplet containing the dilaton-axion field has different R-charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges, mixing gravitational and Yang--Mills instantons with triholomorphic hyperinstantons and axion-instantons. For the tree-level classical special manifolds \(ST(n)=SU(1,1)/U(1)\times SO(2,n)/(SO(2)\) \(\times SO(n))\) R-symmetry with the specified properties is a continuous symmetry, but for the quantum corrected manifolds \({\hat {ST}}(n)\) a discrete R--group of electric--magnetic duality rotations is sufficient and we argue that it exists.

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Confining phase of superstrings and axionic strings

Soo-Jong Rey (1991)

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Special geometry, cubic polynomials and homogeneous quaternionic spaces

B. De Wit, A. Van PROEYEN (1991)

The existing classification of homogeneous quaternionic spaces is not complete. We study these spaces in the context of certain \(N=2\) supergravity theories, where dimensional reduction induces a mapping between {\em special} real, K\"ahler and quaternionic spaces. The geometry of the real spaces is encoded in cubic polynomials, those of the K\"ahler and quaternionic manifolds in homogeneous holomorphic functions of second degree. We classify all cubic polynomials that have an invariance group that acts transitively on the real manifold. The corresponding K\"ahler and quaternionic manifolds are then homogeneous. We find that they lead to a well-defined subset of the normal quaternionic spaces classified by \Al\ (and the corresponding special K\"ahler spaces given by Cecotti), but there is a new class of rank-3 spaces of quaternionic dimension larger than 3. We also point out that some of the rank-4 \Al\ spaces were not fully specified and correspond to a finite variety of inequivalent spaces. A simpler version of the equation that underlies the classification of this paper also emerges in the context of \(W_3\) algebras.