The action for supersymmetric QED is

\begin{align} S_{\text{SQED}} = \int d^4x\left\{8d(x)^2- F_{\mu\nu}(x)F^{\mu\nu}(x) - 4i\lambda(x)\sigma^{\mu}\partial_{\mu}\bar{\lambda}(x)+ |F_L(x)|^2 + |F_{\bar{E}}(x)|^2 \right.\\ + iD_{\mu}^*\bar{\psi}_L(x)\bar{\sigma}^{\mu} \psi_L(x) + iD_{\mu}\bar{\psi}_{\bar{E}}(x)\bar{\sigma}^{\mu} \psi_{\bar{E}}(x) + |D_{\mu}A_L(x)|^2 + |D_{\mu}^*A_{\bar{E}}(x)|^2\\ + ed(x)\left(|A_L(x)|^2 - |A_{\bar{E}}(x)|^2\right) - \frac{e}{\sqrt{2}}[\bar{\lambda}(x)[\bar{\psi}_L(x)A_L(x) - \bar{\psi}_{\bar{E}}(x)A_{\bar{E}}(x)]\\ +\lambda(x)[\psi_L(x)A^*_L(x) - \psi_{\bar{E}}(x)A_{\bar{E}}^*(x)]] - m[A_L(x)F_{\bar{E}}(x) + A_L^*(x)F_{\bar{E}}^*(x)\\ + A_{\bar{E}}(x)F_{L}(x) + A_{\bar{E}}^*(x)F_{L}^*(x) - \left. \psi_L(x)\psi_{\bar{E}}(x) - \bar{\psi}_L(x)\bar{\psi}_{\bar{E}}(x)]\right\}, \end{align} where $A_{L,\bar{E}}$ are selectrons, $\lambda(x)$ is the photino, $\psi_{L,\bar{E}}$ are electrons and $V_{\mu}$ is the photon. The selectrons and electrons have the same mass $m$, while the photon and photino have mass $m=0$. I am breaking this symmetry in the O'Raifeartaigh model which introduces three new scalar fields given by \begin{align} A &= a + \sqrt{2}\theta\psi_A + \theta\theta F_A\\ X &= x + \sqrt{2}\theta\psi_X + \theta\theta F_X\\ Y &= y + \sqrt{2}\theta\psi_Y + \theta\theta F_Y, \end{align} and the superpotential \begin{align} W[A, X, Y] \equiv nAY + gX(A^2 - M^2). \end{align} where $n, g, M\in\mathbb{R}$. This is an example of so called $F$-term breaking of SUSY where one obtains a non-vanishing VEV using the auxiliary field $F_i$.

In the derivation of $\mathcal{L}_{SQED}$, I use three fields: \begin{align} L &= A_L(x) + \sqrt{2}\theta \psi_L(x) + \theta\theta F_L(x),\\ \bar{E} &= A_E(x) + \sqrt{2}\theta \psi_E(x) + \theta\theta F_E(x),\\ V_{WZ}(x, \theta, \bar{\theta}) &= (\theta\sigma^{\mu}\bar{\theta})V_{\mu} + \theta\theta\bar{\theta}\bar{\lambda}(x) + \bar{\theta}\bar{\theta}\theta\lambda(x) + \theta\theta\bar{\theta}\bar{\theta}d(x), \end{align} where $L$ and $\bar{E}$ are lepton superfields while $V_{WZ}$ is the vector superfield in the Wess-Zumino gauge. I only have two scalar fields, while O'Raifeartaigh breaks SUSY spontaneously with three. How can I break the symmetry of the masses in the O'R. model when I'm lacking a scalar field? I'm having a hard time finding sources on this topic as well, any suggestions?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.