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$R$ Parity is a discrete $Z_2 $ symmetry while an $R$ symmetry is a global continuous symmetry. If you use a $Z_2$ symmetry to build your model then each field can just be either odd and even, that's it. If you impose a continuous symmetry then there are an infinite number of possible choices of $R$ charges. From a model building perspective, a continuous ...


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A theory with N=2 supersymmetry, where particles have two superpartners, has mirror symmetry built in. Nir Polonsky wrote some papers about an N=2 extension of the standard model (e.g.). The main problem for such a theory are the chiral Yukawa interactions between fermions and the Higgs field, which give fermions their mass in the SM. The mirror symmetry of ...


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Two-dimensional surfaces are the Feynman diagrams of string theory. In quantum field theory one sums over one dimensional objects in order to calculate quantities like scattering cross sections or decay rates. This is due to the fact that in this framework, particles are represented as zero dimensional objects, i.e. their world lines are points. In ...


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Qmechanic explained a way in which something with the word "commutator" in it doesn't vanish when applied to two of the same operator. However, I feel it is necessary to point out that plain commutators, as seen in a quantum mechanics course, really, honestly, always, and without fail satisfy $[Q,Q] = 0$ for any operator $Q$. This is because $[A,B]$ is ...


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I) Yes, they are probably referring to that a Grassmann-odd operator needs not (super)commute with itself. Take e.g. the 1st order Grassmann-odd differential operator $$\tag{1} D~:=~\frac{d}{d\theta}+ \theta\frac{d}{dt}. $$ In eq. (1) $t$ is a Grassmann-even variable and $\theta$ is a Grassmann-odd variable, which (super)commute $$\tag{2} ...


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For a superfield $S$, an infinitesimal supersymmetric transformation gives : $\delta_\epsilon S = -i(\epsilon\mathcal{Q}+\bar{\epsilon}\bar{\mathcal{Q}})S$ Here $\mathcal{Q}_a$ and ${ \mathcal{\bar Q}}^{\dot a}$ are differential operators applying on the superfield: $\mathcal{Q}_a = i \partial_a - (\sigma^\mu \bar \theta)_a \partial_\mu$, ${ ...


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This terminology is related with spontaneous broken of gauge theory. Higgs mechanics as we are familiar with mass mechanism for gauge boson is related with Higgs phase. and in Coulomb phase gauge boson still exists in massless case and form $\frac{1}{r}$. For $U(1)$ gauge theory it is reduced to coulombic interaction as in electrodynamics.


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I found some interesting papers for $N=2$ by Yuji Tachikawa (N-2 supersymmetric dynamcis for dummies, recently revised to N=2 supersymmetric dynamics for pedestrian : arXiv 1312.2684v2) and some advanced supersymmetric textbook contains extended supersymmetry well. Also these topics are related with Seiberg-witten theory, review papers on Seiberg-witten ...


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In 2d $N=(2,2)^*$ is a reduction of $N=(4,4)$ with some mass condition. The difference between $N=(2,2)$ and $N=(4,4)$ in 2d, can be distinguished by considering 4d $N=1$, $N=2$ theories. (The number of supersymmetric charges are key factor for distinguished them) i.e 4 dimensional $N=1$ supersymmetry has 4 supercharges, and from dimensional reduction, ...



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