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 [1] or [2] 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 ...