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

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,851 answers , 20,616 comments
1,470 users with positive rep
501 active unimported users
More ...

Supersymmetries of the type IIB D3-brane action

+ 4 like - 0 dislike
49 views

The following query is based on a reading of section 2.2 of a paper by Graña and Polchinski. The idea is to begin with the D3 brane action of the form

$$ ds^2 = Z^{-1/2}\eta_{\mu\nu}dx^\mu dx^\nu + Z^{1/2}dx^m dx^n$$

where $\mu, \nu = 0, 1, 2, 3$ and $m, n = 4, 5, \ldots, 9$ are indices along the longitudinal and transverse directions. Also, $\eta_{\mu\nu} = diag(-1, 0, 0, 0)$ and $Z$ is a harmonic function (in the paper it is taken as $Z = R^4/r^4$ where $R^4 = 4\pi g N\alpha'^2$).

Now, type IIB superstring theory has two fermonic superpartners of the NS$\otimes$NS and R$\otimes$R fields, namely the dilatino and the gravitino, the supersymmetry transformations of which are given in terms of a spinor parameter $\epsilon$ in equations (2.1) and (2.2) of the paper. The authors further assert that for bosonic backgrounds, and for constant $\tau = C + i e^{\Phi}$ where $C$ is the axion and $\Phi$ is the dilation, the dilatino variation is trivially zero. I understand this.

But when they set $\delta \psi_M = 0$ ($M = 0, 1, \ldots, 9$) they seem to go from

$$\delta \psi_M = \frac{1}{\kappa}D_M \epsilon + \frac{i}{480}\gamma^{M_1 \ldots M_5}F_{M_1\ldots M_5}\epsilon$$

to

$$k\delta \psi_M = \partial_\mu \epsilon - \frac{1}{8}\gamma_\mu \gamma_w (1 - \Gamma^4)\epsilon$$

where $\Gamma^4 = i \gamma^{0123}$, $w_m = \partial_m \ln Z$ and $\gamma_w = \gamma^m w_m$.

I am not sure how they arrive at this equation. What happened to the $i/480$ term?

This post imported from StackExchange Physics at 2015-04-29 18:25 (UTC), posted by SE-user leastaction
asked Apr 29, 2015 in Theoretical Physics by leastaction (425 points) [ no revision ]
Divide through your second equation by $\kappa$, with $\kappa=8\pi^{7/2}\alpha'^2g$, get $i$ from $\Gamma^4$ and express $\gamma_\omega$ in terms of $\omega_m$.

This post imported from StackExchange Physics at 2015-04-29 18:25 (UTC), posted by SE-user Demosthene
What happened to the product of 5 gamma matrices?

This post imported from StackExchange Physics at 2015-04-29 18:25 (UTC), posted by SE-user leastaction

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:
$\varnothing\hbar$ysicsOverflow
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
...