How can I calculate the F-terms for chiral superfields in a no-scale model?

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In summary, the conversation is about calculating local F-terms for chiral superfields using the Kahler and super-potential equations. The F-terms are given by the covariant derivative of the super-potential, with indices denoting the derivative with respect to the specific field. There is a slight problem with the derivative, but it is resolved by taking the complex conjugate in the case of F*. The conversation also discusses how to determine if the module squared of F is simultaneously zero or not, with equations provided for F_T, F_S, and F_C.
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ChrisVer
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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 F-terms arising from this. The local F-terms for the i-th 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 i-th 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?
 
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  • #2
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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1. What is the "NoScale model F-local term"?

The "NoScale model F-local term" is a mathematical equation used in the field of physics to describe the behavior of a physical system at a small scale, typically at the atomic or subatomic level. It is part of the NoScale model, which is a theory that attempts to explain the fundamental forces of nature.

2. How is the "NoScale model F-local term" different from other models?

The "NoScale model F-local term" differs from other models in that it incorporates the concept of locality, which means that the behavior of a system is only influenced by its immediate surroundings. This is in contrast to other models that may consider non-local effects, such as long-range interactions.

3. Can the "NoScale model F-local term" be applied to all physical systems?

No, the "NoScale model F-local term" is specifically designed to be applied to systems at a small scale, such as atoms and subatomic particles. It is not applicable to larger systems, such as planets or galaxies.

4. How is the "NoScale model F-local term" tested and validated?

The "NoScale model F-local term" is tested and validated through various experiments and observations. These may include particle accelerators, which can recreate the conditions of a small-scale system, and astronomical observations, which can provide evidence for the behavior of systems at a larger scale.

5. What are the implications of the "NoScale model F-local term" for our understanding of the universe?

The "NoScale model F-local term" is still a theoretical concept, and its implications for our understanding of the universe are still being explored. However, if it is proven to accurately describe the behavior of physical systems, it could provide a more comprehensive and unified understanding of the fundamental forces of nature.

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