Lagrangian for a supersymmetric point particle

[jdstokes]

Does anyone know where I can find the lagrangian for this?

From memory I believe it looks something like

S = \frac{1}{2} \int \frac{d\tau}{e}[\dot{X}^2 +i \dot{\psi}{\psi}-2ie\nu \dot{X} \psi]

where e is the graviton and nu is the gravitino. Does anyone know of a reference that supports this?

 

[Haelfix]

That looks correct to me up to constants in front of each term. If you solve the eom you could verify that the constants are correct or not.

 

[jdstokes]

Hi Haelfix,

Thanks for your response. I do not have the equations of motion handy so I was hoping someone might know of a reference which discusses this.

I believe this Lagrangian can be used to motivate the worldsheet Lagrangian in superstring theory.

 

[jdstokes]

For future reference, the answer can be found in problem 4.1 of Becker, Becker and Shwarz.