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I) The gauge transformation of the real gauge field $V$ reads $$\exp(\tilde{V}) ~=~e^Xe^Ve^Y, \qquad X~:=~i\Omega^{\dagger}, \qquad Y~:=~-i\Omega. \tag{1}$$ Keeping only linear orders in $\Omega$, the BCH formula reads $$\tilde{V}~=~B({\rm ad} V)X+V+B(-{\rm ad} V)Y$$ $$~=~V+\frac{1}{2}[V,Y-X]+B_+({\rm ad} V)(X+Y),\tag{2}$$ where  ...

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ADE refers to the ADE classification, which refers to simply-laced simple Dynkin diagrams and corresponding Lie algebra and Lie group. refers to finite subgroups $\Gamma$ of $SU(2)$, which is related to orbifolds $M/\Gamma$, i.e. manifolds with singularities. See also elementary catastrophes. An ADE gauge theory means that the gauge group is an ADE ...

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A more colloquial way of understanding this is to write down the expressions for loop corrections in a SUSY gauge theory. The important ingredient is that in addition to the gauge bosons you will also have gauginos, i.e. fermions in the adjoint representation. To understand how a vacuum diagram vanishes thing about how a gauge boson in 4D has two ...

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So my question is, why can't we mix sneutrinos with Higgses, for instance? Which symmetry would be violated? It seems that the answer is short: This is R-parity. Normal particles (including all 5 Higgs bosons) are R-even and superpartners are R-odd, so they cannot mix if R-parity is unbroken. If it is broken, higgson-sneutrino mixing is possible (and ...

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Wess-Zumino gauge is a particular choice of gauge where the vector superfield has a particular form and has less components than the generic vector super field. So if i'm free to make a gauge transformation i can choose the components of the chiral super field $\Omega$ in a manner that the sum of the $\theta$ (or any other "$\theta$ component" i want to ...

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