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Register a new userExplicit Derivation of New Hyper-Kahler metric
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Authors
Moulay Brahim Sedra
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Using the harmonic superspace techniques in D=2 N=4, we present an explicit derivation of a new hyper-Kahler metric associated to the Toda like self interaction $H ^{4+}(omega, u)= (frac{xi^{++}}{lambda})^{2}exp(2lambda omega)$. Some important features are also discussed.
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It is presented a method of construction of sigma-models with target space geometries different from conformally flat ones. The method is based on a treating of a constancy of a coupling constant as a dynamical constraint following as an equation of motion. In this way we build N=4 and N=8 supersymmetric four-dimensional sigma-models in d=1 with hyper-Kahler target space possessing one isometry, which commutes with supersymmetry.
New heterotic torsional geometries are constructed as orbifolds of T^2 bundles over K3. The discrete symmetries considered can be freely-acting or have fixed points and/or fixed curves. We give explicit constructions when the base K3 is Kummer or algebraic. The orbifold geometries can preserve N=1,2 supersymmetry in four dimensions or be non-supersymmetric.
We analyse the geometry of four-dimensional bosonic manifolds arising within the context of $N=4, D=1$ supersymmetry. We demonstrate that both cases of general hyper-Kahler manifolds, i.e. those with translation or rotational isometries, may be supersymmetrized in the same way. We start from a generic N=4 supersymmetric three-dimensional action and perform dualization of the coupling constant, initially present in the action. As a result, we end up with explicit component actions for $N=4, D=1$ nonlinear sigma-models with hyper-Kahler geometry (with both types of isometries) in the target space. In the case of hyper-Kahler geometry with translational isometry we find that the action possesses an additional hidden N=4 supersymmetry, and therefore it is N=8 supersymmetric one.
We propose an analytic method to calculate the matter field Kahler metric in heterotic compactifications on smooth Calabi-Yau three-folds with Abelian internal gauge fields. The matter field Kahler metric determines the normalisations of the ${cal N}=1$ chiral superfields, which enter the computation of the physical Yukawa couplings. We first derive the general formula for this Kahler metric by a dimensional reduction of the relevant supergravity theory and find that its T-moduli dependence can be determined in general. It turns out that, due to large internal gauge flux, the remaining integrals localise around certain points on the compactification manifold and can, hence, be calculated approximately without precise knowledge of the Ricci-flat Calabi-Yau metric. In a final step, we show how this local result can be expressed in terms of the global moduli of the Calabi-Yau manifold. The method is illustrated for the family of Calabi-Yau hypersurfaces embedded in $mathbb{P}^1timesmathbb{P}^3$ and we obtain an explicit result for the matter field Kahler metric in this case.
This note is an erratum to the paper Tautological classes on moduli spaces of hyper-Kahler manifolds. Thorsten Beckman and Mirko Mauri have pointed to us a gap in the proof of cite[Theorem 8.2.1]{Duke}. We do not know how to correct the proof. We can only recover a partial statement. This gap affects the proof of one of the two main results of cite{Duke}, we explain how to correct it.
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