# Difference between the Rarita-Scwinger field and the gravitino?

+ 2 like - 0 dislike
187 views
The Rarita-Scwhinger field is a spin 3/2 field $\psi_{\mu}^{\alpha}$ but this looks a lot like the gravitons found in string theories, for example it looks like the gravitinos in Ibanez's and Uranga's book of string theory. Therefore why we need two names for the same thing (if the same)? Is its supersymmetry global or local?
asked Jan 4, 2015
recategorized Jan 6, 2015

The graviton we find in string theory and in supergravity in a specific limit is the Rarita-Schwinger field. Specifically in order to get supergravity (let us forget string theory for now) we need to gauge the supersymmetry transformation parameters, i.e. $\epsilon_{\alpha} \to \epsilon_{\alpha}(x)$. Then the associated gauge field is the vector-spinor $\psi_{\alpha \, \mu}$ where $\alpha$ is the internal symmetry index and $\mu$ is the Lorentz index. Now gauging this parameter, which is a constant spinor, we get supergravity which is an interacting theory. The Rarita-Schwinger field is nothing more than the non-interacting or free limit. At this limit the various fields of the theory (which depend a lot on the supersymmetry(ies)) do not interact and we can consider them case by case. Then the vector-spinor field $\psi_{\alpha \, \mu}$ is the Rarita-Schwinger field which transforms in the $$\Big( (1/2, 0) \oplus (0,1/2)\otimes (1/2,1/2) \Big)$$ of the Lorentz group. Just note that general supergravity theories restrict a lot the type of spinor $\psi_{\alpha \, \mu}$ is normally but for a free theory and for any dimension $d$ one can use a complex spinor with $2^{d/2}$ components. A nice review I found was this one where you will find much more (and accurate) info.
 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOverfl$\varnothing$wThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.