Linearizing Generalized Kahler Geometry

The geometry of the target space of an N=(2,2) supersymmetry sigma-model carries a generalized Kahler structure. There always exists a real function, the generalized Kahler potential K, that encodes all the relevant local differential geometry data: the metric, the B-field, etc. Generically this data is given by nonlinear functions of the second derivatives of K. We show that, at least locally, the nonlinearity on any generalized Kahler manifold can be explained as arising from a quotient of a space without this nonlinearity.Comment: 31 pages, some geometrical aspects clarified, typos correcte

Ricci-flat supertwistor spaces

We show that supertwistor spaces constructed as a Kahler quotient of a hyperkahler cone (HKC) with equal numbers of bosonic and fermionic coordinates are Ricci-flat, and hence, Calabi-Yau. We study deformations of the supertwistor space induced from deformations of the HKC. We also discuss general infinitesimal deformations that preserve Ricci-flatness.Comment: 13 pages, references and comments adde

Degeneration of ALF D_n Metrics

Beginning with the Legendre transform construction of hyperk\"ahler metrics, we analyze the ALF version of the D_n metrics. We determine the constraint equation obtained from extremizing the $w$ coordinate of the generating function F(z,\bar{z},u,\bar{u},w) and study its behavior as we send two of the mass parameters of the $D_n$ metric to zero. We find that the constraint equation enforces the limit that the metric becomes that of multi-Taub-NUT.Comment: 14 pages, 7 figures, LaTeX, minor corrections, to appear in JHE

Noncommutative Solitons: Moduli Spaces, Quantization, Finite Theta Effects and Stability

We find the N-soliton solution at infinite theta, as well as the metric on the moduli space corresponding to spatial displacements of the solitons. We use a perturbative expansion to incorporate the leading 1/theta corrections, and find an effective short range attraction between solitons. We study the stability of various solutions. We discuss the finite theta corrections to scattering, and find metastable orbits. Upon quantization of the two-soliton moduli space, for any finite theta, we find an s-wave bound state.Comment: Second revision: Discussions of translation zero-modes in section 4 and scales in section 5 improved; web addresses of movies changed. First revision: Section 6 is rewritten (thanks to M. Headrick for pointing out a mistake in the original version); some references and acknowledgements added. 21 pages, JHEP style, Hypertex, 1 figure, 3 MPEG's at: http://www.physto.se/~unge/traj1.mpg http://www.physto.se/~unge/traj2.mpg http://www.physto.se/~unge/traj3.mp

A note on area variables in Regge calculus

We consider the possibility of setting up a new version of Regge calculus in four dimensions with areas of triangles as the basic variables rather than the edge-lengths. The difficulties and restrictions of this approach are discussed.Comment: 4 pages, amstex. Revision has minor changes and more precise conclusion

Generalized Calabi-Yau metric and Generalized Monge-Ampere equation

In the neighborhood of a regular point, generalized Kahler geometry admits a description in terms of a single real function, the generalized Kahler potential. We study the local conditions for a generalized Kahler manifold to be a generalized Calabi-Yau manifold and we derive a non-linear PDE that the generalized Kahler potential has to satisfy for this to be true. This non-linear PDE can be understood as a generalization of the complex Monge-Ampere equation and its solutions give supergravity solutions with metric, dilaton and H-field.Comment: 26 page

Superspace WZW Models and Black Holes

We show how to write an off-shell action for the $SU(2)\times U(1)$ supersymmetric WZW model in terms of $N=2$ chiral and twisted chiral multiplets. We discuss the $N=4$ supersymmetry of this model and exhibit the $N=4$ superconformal current algebra. Finally, we show that the off-shell formulation makes it possible to perform a duality transformation, which leads to a supersymmetric sigma model on a manifold with a black hole type singularity.Comment: 12 page