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NoScale model Flocal term 
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#1
Jun1914, 07:01 PM

P: 751

In case you have the Kahler and super potential [itex]K,W[/itex]:
[itex] K(T,S,C) = log (S +S^{*}) 3 log ( T+ T^{*}  C C^{*}) [/itex] [itex] W(T,S,C)= C^{3} + d e^{aS} +b [/itex] with [itex]T,S,C[/itex] chiral super fields, [itex]b,d[/itex] complex numbers and [itex]a>0[/itex]. I tried to calculate the local Fterms arising from this. The local Fterms for the ith chiral superfield are given by: [itex] F_{i}= D_{i}W = K_{i}W + W_{i}[/itex] where in the rhs the index i denotes the derivative wrt to the ith field. eg [itex]W_{S}=\frac{\partial W}{\partial S}[/itex] However I'm having a slight problem with the particular derivative. See what I mean...taking it: [itex] F_{S}= K_{S} W + W_{S} =  \frac{C^{3} + d e^{aS} +b}{S+S^{*}} d a e^{aS}[/itex] correct? On the other hand, if I try to work with the covariant derivative wrt to the conjugate fields: [itex] F^{*}_{S}= D_{S^{*}} W^{*} = K_{S^{*}} W^{*} + W_{S^{*}} [/itex] I don't get the complex conjugate of the above. Because in this case [itex]W_{S^{*}}=0[/itex] and so: [itex] F^{*}_{S}=  \frac{(C^{3} + d e^{aS} +b)^{*}}{S+S^{*}}[/itex] what's the problem? 


#2
Jun1914, 07:05 PM

P: 751

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 [itex]F[/itex] let's say... How can I see if its module squared is simultaneously zero or not? [itex] F_{T}^{2}= \frac{9}{(T+T^{*}  CC^{*})^{2}} C^{3}+ d e^{aS} +b ^{2} [/itex] [itex] F_{S}^{2}=  \frac{C^{3} + d e^{aS} +b}{S+S^{*}} + d a e^{aS}^{2} [/itex] [itex] F_{C}^{2}=  \frac{3 C^{*} (C^{3}+d e^{aS} +b)}{T+T^{*}CC^{*}} +3 C^{2}^{2} [/itex] 


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