# Questions tagged [superspace-formalism]

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

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4answers
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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 ...
2answers
2k views

### 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 ...
2answers
2k views

1answer
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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 ...
1answer
444 views

### 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 ...
1answer
395 views

### 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 ...
0answers
119 views

0answers
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### 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
49 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 ...
3answers
245 views

### 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?
0answers
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### 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
39 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
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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 ...
1answer
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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 ...
1answer
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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 ...