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On the top of page 23 of hep-th/03061119, it is pointed out that treating the holomorphic gauge coupling $\tau$ as a background (spurion) superfield allows one to think of its $F$-term, $F_\tau$ as the source for the gaugino condensate, $\lambda^a\lambda^a$. This is because in the supersymmetric gauge kinetic term,

$\mathcal L \supset \int \tau \mathcal{W}^a\mathcal{W}_a$,

$F_\tau$ is the coupling for the $\lambda^2$ term. I think I understand how this acts as a constant source for $\lambda^2$ 'tadpoles', but I don't undertand why the $\theta^0$ term of $\tau$ (i.e. the lowest component of the background superfield, the gauge coupling itself) shouldn't also be thought of as a source for $F^2$.

It makes sense to me that $F^2$ is just the usual gauge kinetic term and its coefficient is related to the gauge coupling. However, why is this term any different from the $\lambda^2$ term: why should $F_\tau$ be thought of as a source for a gaugino condensate whereas $\tau$ shouldn't be thought of as a source for a gluon condensate?

Thanks!

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