Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

146 submissions , 123 unreviewed
3,953 questions , 1,403 unanswered
4,889 answers , 20,761 comments
1,470 users with positive rep
506 active unimported users
More ...

Substitution in the following supersymmetry transformation rule

+ 2 like - 0 dislike
65 views

I was reading in this book: Supergravity for Daniel Freedman and was checking the part that has to do with Extremal Reissner Nordstrom Black Hole. He was using killing spinors (that I am very new to).

I was understanding the theory until he stated with the calculations:

He said that the Supersymmetry transformation (21.49) in his book is:

$$\delta \psi_\mu^i=(\partial_\mu +1/4 \gamma^{ab}\omega_{\mu ab})\epsilon^i -1/8\sqrt{2}\kappa \gamma^{ab}F_{ab}\epsilon^{ij} \gamma_\mu \epsilon_j$$

He then started "It is convenient to work with the chiral projections of the two Majo-rana spinors. We thus use the up/down position of the R-symmetry indices, now denoted by (A, B=1, 2), to specify the chirality. Thus, for the SUSY transformation parameters, we have"

$\gamma_* \epsilon^A= P_L \epsilon^A = \epsilon^A$ and $\gamma_* \epsilon_A= - P_R \epsilon_AA = - \epsilon_A$ where $\gamma_*$ is the usual $\gamma_5$ and $P_L$ and $P_R$ are projection operators to define chiral parts.

So back to the first equation that I wrote here: He substituted it with: $$ \delta \psi_{tA} = \partial_t \epsilon _A +1/2 e^{2U} \partial_i U\gamma^i \gamma^0 \epsilon_A -1/4 \sqrt{2}\kappa e^u \partial_i A_t \gamma^i \epsilon_{AB} \epsilon^b =0$$

It is specifically the substitutions that I could not follow, where did the gamma matrices in the last equation come from?

Concerning the spin conection I found them to be: $\omega^{0i} = e^U \partial_iU e^0$ and $\omega ^{ij} = -dx^i\partial_jU+dx^j\partial_iU$ and they each have 2 indices while in the supersymmetry transformation equation the omega has 3 indices. I know I am missing something and I hope you can help me understand the substitution better.

This post imported from StackExchange Physics at 2014-12-01 21:47 (UTC), posted by SE-user Fluctuations
asked Dec 1, 2014 in Theoretical Physics by Fluctuations (10 points) [ no revision ]

Your answer

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):
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$\hbar$ysics$\varnothing$verflow
Then 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.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...