I am struggleing in an identity, i.e. [tex]\nabla_m R_{ikjl}(\overline{\epsilon}\psi^m)(\overline{\psi^i}\psi^j)(\overline{\psi^k}\psi^l)=0[/tex] ,(adsbygoogle = window.adsbygoogle || []).push({});

where [tex]i,j,k,l,m[/tex] are dummy indices, [tex]\nabla_m[/tex] is covariant derivative, [tex]R_{ikjl}[/tex] is Riemann-Christoffel curvature tensor, and it is known that, for any two arbitary spinors [tex]\psi^i,\psi^j[/tex], [tex]\overline{\psi^i}\psi^j=\overline{\psi^j}\psi^i[/tex].

I think one could use Bianchi Identity to prove this, but I failed.....who can do me a favor? Thanks!

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# An Identity in SUSY sigma model

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