- #36

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Can you design a fundamental force of nature that has same symmetry breaking mechanism as proposed for SUSY

The fact that positive vacuum energy reflects spontaneous supersymmetry breaking is a direct consequence of the fact that local supersymmetry is an extension of local Poincaré symmetry, hence of gravity. Technically, this is because the stress-energy tensor ##(T_{\mu \nu})## in supersymmetric field theories is the image of the supersymmetry Noether's conserved current ##(S_{\nu \beta})## under the super-Poisson-bracket with the supercharge ##(Q_\alpha)##

$$

T_{\mu \nu}

\;=\;

\gamma_\mu^{\alpha \beta}

\{Q_\alpha, S_{\nu,\beta}\}

$$

so that the vacuum expectation value of the stress-energy tensor is

$$

\langle vac \vert

T_{\mu \nu}

\vert vac \rangle

=

\gamma_\mu^{\alpha \beta}

\langle vac \vert

\{Q_\alpha, S_{\nu,\beta}\}

\vert vac \rangle

$$

which hence vanishes if the vacuum state is supersymmetric, hence if supersymmetry is not spontaneously broken.

So the specific nature of spontaneous supersymmetry-breaking is a reflection of the special fact that (local) supersymmetry is an odd-graded extension of (local) Poincaré-symmetry, hence of gravity. Symmetries not related to gravity in such a way cannot show this effect.

I recommend going to the original articles, such as Witten 81, section 2. The graphics that you reproduce above originates in Fayet-Ferrara 77, Fig. 1 on p. 286 (38 of 86).