term on the RHS in . As discussed in the previous section, at least as long as we do not include a superpotential term for the chiral superfield $S$ in the chiral multiplet form (CMF) action[^4], the linear multiplet form is equivalent to the chiral multiplet form. According to the discussion there, the gauge coupling function (at $\mu^{2}=M_{string}^{2}$) is to be interpreted initially in the LMF, i.e. the model . Here $U$ should correspond to the dilaton in the linear multiplet formulation which to zero loop order can be identified as $-(3\Re S)^{-1}$. The term $V$ in is identified with $\frac{\Delta^{univ}(M,\bar{M})}{16\pi^{2}}$. In the corresponding chiral multiplet formulation (in terms of $S$) the instruction implied by this is in effect to drop this term from the expression for the coupling function (thus identifying at the high scale $g_{a}^{-2}=k_{a}\Re S$) but include it as a one-loop correction to $K$ (see) with $$K=-\ln(S+\bar{S}+\frac{\Delta^{univ}(M\bar{M})}{16\pi^{2}})+\hat{K}(M,\bar{M}).\label{eq:K1lphet}$$

Note that if one makes the above correction to $K$ and then plugs that back into the CMF form of the action , then all that changes in the KL formula is the explicit expression for the term $\frac{c_{a}}{16\pi^{2}}K(\Phi,\bar{\Phi})$ which now becomes $\frac{c_{a}}{16\pi^{2}}$ times the RHS of . However in 