Kahler-Einstein and Kahler scalar flat supermanifolds
| Autor: | Ang, J. P., Rocek, Martin, Schulman, John |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | Two results regarding K\"ahler supermanifolds with potential $K=A+C\theta\bar\theta$ are shown. First, if the supermanifold is K\"ahler-Einstein, then its base (the supermanifold of one lower fermionic dimension and with K\"ahler potential $A$) has constant scalar curvature. As a corollary, every constant scalar curvature K\"ahler supermanifold has a unique superextension to a K\"ahler-Einstein supermanifold of one higher fermionic dimension. Second, if the supermanifold is itself scalar flat, then its base satisfies the equation $$ \phi^{\bar ji}\phi_{i\bar j}=2\Delta_0 S_0 + R_0^{\bar ji}R_{0i\bar j} - S_0^2, $$ where $\Delta_0$ is the Laplace operator, $S_0$ is the scalar curvature, and $R_{0i\bar j}$ is the Ricci tensor of the base, and $\phi$ is some harmonic section on the base. Remarkably, precisely this equation arises in the construction of certain supergravity compactifications. Examples of bosonic manifolds satisfying the equation above are discussed. Comment: 9 pages--reference and examples added |
| Databáze: | arXiv |
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