# NoScale model F-local term

by ChrisVer
Tags: flocal, model, noscale, term
 P: 890 In case you have the Kahler and super- potential $K,W$: $K(T,S,C) = -log (S +S^{*}) -3 log ( T+ T^{*} - C C^{*})$ $W(T,S,C)= C^{3} + d e^{-aS} +b$ with $T,S,C$ chiral super fields, $b,d$ complex numbers and $a>0$. I tried to calculate the local F-terms arising from this. The local F-terms for the i-th chiral superfield are given by: $F_{i}= D_{i}W = K_{i}W + W_{i}$ where in the rhs the index i denotes the derivative wrt to the i-th field. eg $W_{S}=\frac{\partial W}{\partial S}$ However I'm having a slight problem with the particular derivative. See what I mean...taking it: $F_{S}= K_{S} W + W_{S} = - \frac{C^{3} + d e^{-aS} +b}{S+S^{*}} -d a e^{-aS}$ correct? On the other hand, if I try to work with the covariant derivative wrt to the conjugate fields: $F^{*}_{S}= D_{S^{*}} W^{*} = K_{S^{*}} W^{*} + W_{S^{*}}$ I don't get the complex conjugate of the above. Because in this case $W_{S^{*}}=0$ and so: $F^{*}_{S}= - \frac{(C^{3} + d e^{-aS} +b)^{*}}{S+S^{*}}$ what's the problem?
 P: 890 Ah found the mistake.... again by writing in LaTeX it became obvious- In the F* equation I needed the W* derivative as the second term... However In the case of $F$ let's say... How can I see if its module squared is simultaneously zero or not? $|F_{T}|^{2}= \frac{9}{(T+T^{*} - CC^{*})^{2}} |C^{3}+ d e^{-aS} +b |^{2}$ $|F_{S}|^{2}= | \frac{C^{3} + d e^{-aS} +b}{S+S^{*}} + d a e^{-aS}|^{2}$ $|F_{C}|^{2}= | \frac{3 C^{*} (C^{3}+d e^{-aS} +b)}{T+T^{*}-CC^{*}} +3 C^{2}|^{2}$