I'm currently trying to read a paper and it's not making much sense. Don't feel I expect anyone to read it in detail but it might give you an idea of the lack of understanding I am having. In all honesty I don't think it's terribly well written, coupled with the fact that I'm thick and only half know what I'm doing. The paper is....
Lars Brink et al 'N=4 yang mills theory on the light cone' nucl phys B212(1983) 401412.
They write a scalar superfield as follows
[tex]\Phi(x,\theta)=\frac{1}{\partial^+}A(y)+i{\partial_+}\theta^m\bar{\chi}_{m}(y)+\sqrt{1/2}i\theta^{m}\theta^{n}\bar{C}_{mn}(y)+\frac{1}{6}\sqrt{2}\theta^m\theta^n\theta^p \epsilon_{mnpq}\chi^{q}+\frac{1}{12}\theta^{m}\theta^{n}\theta^{p}\theta^{q}\epsilon_{mnpq}\partial^{+}\bar{A}(y)[/tex]
Where [tex]\partial^+[/tex] is just the derivative in light cone coords, that's not a problem. A(y) is the vector component (but it's in the light cone gauge so A and its conjugate are just scalars) [tex]\chi[/tex] is the spinor component and [tex]\bar{C}_{mn}[/tex] is a matrix of the 6 real scalar fields and is anti symmetric in m and n. m and n run from 1 to 4 and [tex]\theta[/tex] are grassman numbers.
y is given by [tex]y=(x,\bar{x},x^+,x^{}\sqrt{1/2}i \theta^m \bar{\theta_{m}})[/tex]
It does not say if the [tex]\theta[/tex]s are majorana spinors or not, and contracting the m indices like that in the expression for y doesn't make sense to me anyway. Isn't there supposed to be a gamma matrix in between?
Basically I want to taylor expand all the components fields so they are in terms of x, not y so I can repeat their calculations for myself. Any hints or help is appreciated. This is the first time I have studied SUSY in detail. I know the basics.
Lars Brink et al 'N=4 yang mills theory on the light cone' nucl phys B212(1983) 401412.
They write a scalar superfield as follows
[tex]\Phi(x,\theta)=\frac{1}{\partial^+}A(y)+i{\partial_+}\theta^m\bar{\chi}_{m}(y)+\sqrt{1/2}i\theta^{m}\theta^{n}\bar{C}_{mn}(y)+\frac{1}{6}\sqrt{2}\theta^m\theta^n\theta^p \epsilon_{mnpq}\chi^{q}+\frac{1}{12}\theta^{m}\theta^{n}\theta^{p}\theta^{q}\epsilon_{mnpq}\partial^{+}\bar{A}(y)[/tex]
Where [tex]\partial^+[/tex] is just the derivative in light cone coords, that's not a problem. A(y) is the vector component (but it's in the light cone gauge so A and its conjugate are just scalars) [tex]\chi[/tex] is the spinor component and [tex]\bar{C}_{mn}[/tex] is a matrix of the 6 real scalar fields and is anti symmetric in m and n. m and n run from 1 to 4 and [tex]\theta[/tex] are grassman numbers.
y is given by [tex]y=(x,\bar{x},x^+,x^{}\sqrt{1/2}i \theta^m \bar{\theta_{m}})[/tex]
It does not say if the [tex]\theta[/tex]s are majorana spinors or not, and contracting the m indices like that in the expression for y doesn't make sense to me anyway. Isn't there supposed to be a gamma matrix in between?
Basically I want to taylor expand all the components fields so they are in terms of x, not y so I can repeat their calculations for myself. Any hints or help is appreciated. This is the first time I have studied SUSY in detail. I know the basics.
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