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What is supersymmetry (in a big nutshell)? To explain supersymmetry, let us consider the simplest supersymmetric model which is the Wess-Zumino model with an action, $$S=-\int d^4x \left( \frac{1}{2}\partial^\mu \phi^\star \partial_\mu \phi + i\psi^\dagger \bar{\sigma}^\mu \partial_\mu \psi + |F|^2 \right)$$ where $\phi$ is a scalar field, $\psi$ a ...


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An R-symmetry is any global symmetry that transforms the supercharge or supercharges – often in a theory with extended supersymmetry, one in which the supersymmetry generators $Q_i^\alpha$ carry an extra internal index $i$ – into each other. It is typically $U(1)$ for non-extended $N=1$ supersymmetry and becomes non-Abelian, like $SU(2)$ or $SU(4)$, in ...


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Here is a partial answer: Define $Sp(2N,\mathbb{R})$ as the group of matrices $S$ such that $S \cdot\Omega\cdot S^T=\Omega$ where $\Omega_{ij}$ is a non-degenerate anti-symmetric matrix. Then $\Omega_{ij}$ is an invariant tensor similar to the Kronecker delta for orthogonal transformations. I don't think there are any more (not 100% sure). For $E_7$: $E_7$ ...


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Just realize that you can form ordinary Dirac spinors from 2-spinors by using charge conjugation, $i\sigma_2\eta^*$, that gives a right- handed field that can fit in the right-handed slot (forming a 4 component Majorana field) $$ \Psi_1=\left(\begin{array}{c}\eta \\ i\sigma_2\eta^*\end{array}\right) $$ And analogous for $\Psi_2$ in terms of $\chi$. Then you ...


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The gluino does indeed change QCD, however as you probably can guess its a very small modification. A gluino pair is able to pop in and out of the vacuum and will also change the interaction between two quarks. However, due to its necessarily large mass it won't be a large effect. Also since it is a fermion it can't interact directly will quarks (it must go ...


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Let us take a few steps back and try to understand why that statement from Wikipedia is correct. To see this we have to first understand the coupling of the graviton to matter particles. The graviton couples to matter via its energy-momentum tensor $\sim g_{\mu\nu}T^{\mu\nu}.$ The energy momentum tensor is a response to the variations of the metric ...



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