Tag Info

New answers tagged

3

TL;DR: It is the wedge product $\wedge$ and the exterior derivative/differential $d$ (which squares to zero $d^2=0$) that give rise to Grassmann-odd elements and supersymmetry. More concretely, Ref. 1 first writes down a (non-relativistic) SUSY algebra ${\cal A}$ $$\tag{10} \{Q_1,Q_1\}_+~=~2H~=~\{Q_2,Q_2\}_+, \qquad \{Q_1,Q_2\}_+~=~0, $$ spanned by two ...


1

A priori, it is hard to know without having any experience with dimensional reductions. One has to get a feeling for how certain quantities change under the process, e.g. how components of the higher-dimensional gauge fields may turn into adjoint scalars, how spinors behave. An interesting thing to note is that symmetries of the lower-dimensional theory ...


2

A bosonic symmetry that acts differently on the different components of a supermultiplet is an R-symmetry. Such a symmetry does not commute with the supercharges. Since the commutator between an R-symmetry and a supercharge gives something Grassmann odd, it has to given another supercharge. Schematically $$ [R,Q] = Q $$ or in terms of variations acting on ...


0

The ten-dimensional case is explained in some detail in appendix 4.A of volume one of Green-Schwarz-Witten. Let me therefore consider the 4d case here. The calculation works essentially the same in 3d, 6d and 10d, though you can sometimes make use of Majorana and/or Weyl conditions of the spinors to simplify things. We want to check that the expression ...


0

When people talk about $\mathcal{N}=2$ QED in 4d I think they normally mean a $U(1)$ gauge theory (one $\mathcal{N}=2$ vector multiplet) coupled to one or more hypermultiplets (usually all with the same $U(1)$ charge). As an example of this usage see Witten's discussion of $\mathcal{N}=4$ QED in 3d (which can be obtained by dimensional reduction from the ...


1

Yes, you are correct. $\mathcal{N}=2$ supersymmetry in 3d can be obtained by dimensionally reducing 4d $\mathcal{N}=1$. The 4d chiral superfield contains a complex scalar, a Weyl fermion, and a complex auxiliary field. Reducing this to 3d we get a compex scalar, a Dirac fermion, and the auxiliary. You can also impose reality conditions to rewrite the 4d ...



Top 50 recent answers are included