Timeline for Geometric origin of the Kahler potential for SUSY $\sigma$-models

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Apr 22, 2019 at 5:20	history	edited	Andrey Feldman	CC BY-SA 4.0	edited body
Dec 14, 2016 at 9:51	vote	accept	Bulkilol
Dec 13, 2016 at 19:37	comment	added	Andrey Feldman		@Such a structure can be constructed from the covariant spinors on the target space, which existence is guaranteed by the presence of supersymmetry. Schematically, for the case of $\cal{N}=1$ and covariant spinor $\eta$, the Kahler form and the volume form have the form: $\omega_{\mu \nu}=\eta \Gamma_{\mu \nu} \eta$, $\Omega_{\mu \nu \rho}=\eta \Gamma_{\mu \nu \rho} \eta$. See, for example, the seminal paper "Vacuum configurations for superstrings" by Witten et al.
Dec 13, 2016 at 17:25	comment	added	Bulkilol		Indeed, I didn't realise that the result is valid only in 2 and 3 dimensions. However, I still have a question: If I start with the first Lagrangian in four dimensions and I stay completely agnostic about superspace. Is it possible to prove starting only from supersymmery transformations that there is a complex structure I^2?
Dec 12, 2016 at 14:21	history	answered	Andrey Feldman	CC BY-SA 3.0