# Questions tagged [superspace-formalism]

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

34 questions
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### 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?
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### What are Grassmann numbers in field theory?

I've been struggling with the use of Grassmann numbers in QFT e.g. Peskin and Schroeder. They are introduced as "numbers" whose product is antisymmetric, and associative (this isn't said, but used in ...
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### ${\cal N} = 1$ SUSY Non-renormalization theorem

In Ref. 1, on Page 53, the ${\cal N} = 1$ SUSY non-renormalization theorem is derived. One first specifies the symmetries of the general ${\cal N} = 1$ SUSY action in the superspace formalism, and ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 2D ${\cal N}=(2,2)$ Super Yang-Mills with Superspace

I'm reading this famous paper by Witten. There is the expression of field strength for the abelian vector multiplet (eq. (2.16)): $$\Sigma = \frac{1}{\sqrt{2}}\bar{D}_+D_- V\;.\tag{2.16}$$ I'm ...
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### Are there SUSY Lagrangian terms that are not D-term nor F-term?

I've read that a way to construct supersymmetric invariant lagrangian could be either to integrate a superfield in the whole superspace, i.e. in all anticommuting coordinates (D-term), or in half of ...
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### Supergravity action as a total integral, over 4 spacetime and 4 Grassmann coordinates

Wess and Bagger, in their Supersymmetry and Supergravity, give the action for a global SUSY, ${\cal N}=1$, $D=4$, Yang-Mills gauge model as an integral over the 4 spacetime coordinates and 4 Grassmann ...
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### Super Field Strength Identity

I work on a introduction into Super-symmetry. In the course we define \begin{equation} D_{\alpha} = \frac{\partial}{\partial \theta^{\alpha}} - i \sigma^{\mu}_{\alpha \dot{\alpha}} \bar{\theta}^{\dot{\...
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### Ambiguity of Time Derivative of Superfunctions

I think that there is an ambiguity for defining the time derivative of a superfunction on the phase space of pseudo-classical mechanics of Grassmann numbers. Let $\xi$ be a Grassmann odd number. Its ...
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### Questions about the Ferrara-Zumino Multiplet

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 ...
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### What is the definition of $\delta^{m|n}$ and $\delta^{m}$?

I am reading the paper. What is the definition of $\delta^{m|m}$ and $\delta^{m+k}$ in (1.1) and (1.3) on pages 2,3? Are they some kind of delta function?
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### Grassmann numbers & supermanifolds

I'm asking this question because I'm currently trying to learn about Super Symmetry but I'm having trouble understanding the concept of super-space and super-manifold. I read that in super-spaces you ...
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### Should the complex conjugate of a derivative of a Grassmann number include a sign?

Take a real Grassmann variable, by which I mean $\theta=\theta^*$. We have $$\int d\theta~ \theta =1,\qquad \frac{\partial}{\partial\theta}\theta=1$$ If I define the conjugation of Grassmann ...
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### Fayet-Iliopoulos terms

It is mentioned in first page of this paper by Seiberg and Komargodski that the Lagrangian in superspace of a $U(1)$ gauge SUSY theory with FI terms is not gauge invariant. However, the FI terms in ...
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### 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 ...
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### 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 ...
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### Basic question about superspace, Grassmann numbers and world sheet supersymmetry

So, I'm trying to read the section on superspace from the book on string theory by Becker, Becker and Schwarz, and I realized that I've been stuck on something simple for a while. Some relevant ...
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### Supersymmetry transformations as coordinate transformations

Usually, a supersymmetry transformation is carried out on bosonic and fermionic fields which are functions of the coordinates (or on a superfield which is a function of real and fermionic coordinates)....
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### Relation between $\mathcal{N}=2$ d=4 SUSY and $\mathcal{N}=4$ d=3 SUSY

What is meant with the fact that supersymmetry with $\mathcal{N}=4$ in three (2+1) dimensions is equivalent to supersymmetry with $\mathcal{N}=2$ in ordinary four (3+1) dimensions? Which way does one ...
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### Are there two types of D-term and two types of F-term in SUSY?

I've noticed that one can obtain D-terms either by integrating a vector superfield (the vector multiplet) over superspace or by integrating a Kahler potential over superspace. In both cases we get ...
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### 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 ...
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### Grassmann paradox weirdness

I'm running into an annoying problem I am unable to resolve, although a friend has given me some guidance as to how the resolution might come about. Hopefully someone on here knows the answer. It is ...
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### Kähler potential vs full effective potential

In evaluating the vacuum structure of quantum field theories you need to find the minima of the effective potential including perturbative and nonperturbative corrections where possible. In ...