Register to reply

NoScale model F-local term

by ChrisVer
Tags: flocal, model, noscale, term
Share this thread:
ChrisVer
#1
Jun19-14, 07:01 PM
P: 919
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?
Phys.Org News Partner Physics news on Phys.org
Engineers develop new sensor to detect tiny individual nanoparticles
Tiny particles have big potential in debate over nuclear proliferation
Ray tracing and beyond
ChrisVer
#2
Jun19-14, 07:05 PM
P: 919
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]


Register to reply

Related Discussions
Weih's data: what ad hoc explanations do local and non-local models give? Quantum Physics 60
Gravity term in simple 2 DOF quarter car model? Automotive Engineering 3
Term structure isomorphic to the usual model/structure of number theory Set Theory, Logic, Probability, Statistics 2
Local deterministic model of singlet state correlations Quantum Physics 0
Currentday misuse of the term Model General Discussion 18