Explicit Ricci-flat Kähler metrics on cones over products of projective spaces are built from gauged linear sigma models whose 'shadow' fields carry negative-signature kinetic terms.
All toric Kahler surfaces with twistor 2-forms
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We complete the classification of all smooth 4-dimensional Kahler geometries admitting a twistor (conformal Killing-Yano) 2-form invariant under a 2-torus action. We establish that there are six geometrically distinct families, and we provide them in a simple form amenable to calculations and compute their curvature. We also find that for toric geometries the square norm of the twistor 2-form is quadratic in moment maps, and we are led to conjecture that this holds when less symmetry is present.
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Ricci-flat metrics from gauged linear $\sigma$-models without RG flow
Explicit Ricci-flat Kähler metrics on cones over products of projective spaces are built from gauged linear sigma models whose 'shadow' fields carry negative-signature kinetic terms.