the way up to and beyond the string scale. The argument for the necessity of certain field redefinitions that result from this comparison are then very sensitive to exactly where the cutoffs are located, and can be changed by appropriately choosing the cutoffs at scales below the string scale. Finally we resolve a long standing puzzle regarding two different derivations of the non-perturbative (gaugino condensate) term in the superpotential.

General framework
=================

Linear -chiral duality $ $with $\partial_{S}W=0$.
-------------------------------------------------

As mentioned earlier the linear multiplet - chiral multiple duality has been discussed for example in [@Derendinger:1991hq] and [@Binetruy:2000zx](BGG). We essentially follow the discussion of BGG except that the Kaehler supergravity framework is replaced by the standard (minimal) one. We begin with the following action (with $\kappa=M_{P}^{-1}=1,\, d^{8}z=d^{4}xd^{4}\theta,\, d^{6}z=d^{4}xd^{2}\theta$) for chiral superfields $\Phi$ (having superpotential $W$ and Kaehler potential $K$) coupled to supergravity and gauge fields with prepotential $V$ and gauge field strength ${\cal W}$. $$\begin{aligned}
{\cal A} & = & -3\int d^{8}z{\bf E}\exp[-\frac{1}{3}K(\Phi,\bar{\Phi};V)]\nonumber \\
 &  & +\left(\int d^{8}z\frac{{\bf E}}{2R}[W(\Phi)+\frac{1}{4}f(\Phi){\cal W}{\cal W}]+h.c.\right).\label{eq:action}\end{aligned}$$ Here ${\bf E}$ is the full superspace superdeterminant and $R$ is the chiral superspace curvature. Note that the gauge coupling function $f$ is in general a *holomorphic* gauge invariant 