Questions tagged [superspace-formalism]

The Green-Schwarz formalism, or the superspace-formalism, are formalisms for supersymmetry with explicit spacetime supersymmetry.

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To quantize a theory, Klein gordon field for example, commutation relations are stablished. Or anticommuting ones in the fermionic case. If I have the Wess.Zumino model or the free model: $$S~=~\int\... 1answer 83 views Auxiliary Grassmann variables in supergeometry I was reading on super geometry and how it is used to model fermions and supersymmetry in classical field theory. In texts like  or  the authors introduced auxiliary Grassmann odd variables to ... 0answers 157 views Projective superspace: why extra bosonic coordinates I'm studying the projective superspace formalism for N = 4 supersymmetric \sigma-models in two dimensions. My question is: why do we need the extra bosonic coordinates for the manifest action? I ... 0answers 177 views What mathematical structure describes superspace and superfields? In every book related to supersymmetry I have encountered at some point the idea of superspace is introduced. Superspace is presented as a space spanned by 4 "normal" directions and 4 Grassmannian ... 0answers 226 views Can mass dimension of a field be viewed as another 'quantum number'? While studying SUSY in 4D, I noticed the dynamical chiral superfield has dimension [GeV], whereas the dynamical vector superfield (for gauge theories) is unitless. Because I was introduced to the ... 1answer 54 views Could you get real space from Grassmann numbers? You can get a vector field from a pair of spinor fields with A_\mu(x)=\psi(x) \gamma_\mu \overline{\psi}(x). Using this fact could you define a space-time vector in terms of Grasman numbers? Say ... 0answers 28 views Supersymmetry Generator Definition for {\cal N }= 1 I am studying SYM \mathcal{N} = 1 in D = 10, and using the bimodular representations for the 32x32 gamma matrices \Gamma^a. This means that I work with the off-diagonal 16x16 matrices, which I ... 0answers 51 views Super-gauge transformation in two dimensional \mathcal{N}= (0,2) superspace I'm trying to couple matter to \mathcal{N}=(0,2) SYM in 2d using superfield formalism. There are some paper (this on Sec. 6, or this on Sec. 3 [whose notation will be used here]) that construct what ... 0answers 16 views Determination of Torsion constraints in {\cal N} = 1, D = 10 Superspace For the on-shell theory, containing the graviton e_m^{\ \ \ a}, gravitino \psi_m^{\ \ \ \alpha}, dilaton \phi, dilatino \lambda and 3-form H_{n m p}, one has to demand that the SUSY algebra ... 1answer 41 views Anti-Commutator of derivatives of Grassmann variables How do I evaluate the anti-commutator of \frac{\partial}{\partial\chi} and \frac{\partial}{\partial\eta} when both \chi and \eta are Grassmann variables? 1answer 38 views Grassmann-odd extra dimensions and gravity Take a world with D=3+n space-time dimensions, where n are extra space-like dimensions. With extra-dimensional newton gravity$$F=G_N(D)\dfrac{Mm}{r^{2+n}} Can $n$ affect IF the extra ...
These questions arose while reading the paper Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity" by Komargodski and Seiberg (arXiv:1002.2228) The Ferrara-Zumino ...
Why is the mass dimension of anticommutingcoordinates $[Mass]−1/2$
I am reading a review about supersymmetry and in page 29 I have read that the mass dimension of the Grassmann anticommuting coordinates is $-1/2$. Why this? why don't they have the same mass ...