I am reading the paper http://arxiv.org/abs/hep-th/9701037.(adsbygoogle = window.adsbygoogle || []).push({});

In equation (2), the author write the determinat as traces, but I don't know how to do this.

I know that ##det(e^A)=e^{tr(A)}##, where ##A## is a complex matrix, and ##det(A)=e^{tr(L)}##, where ##e^L=A## and ##L## is also a complex matrix.

The problem becomes how to find the logrithm of the matrix ##g_{mn}+i##[itex]\tilde{F}_{mn}[/itex].

Above is what I can figure out now.

Any help would be vary appreciated!

Regards.

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# Writing determinant as traces

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