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

PO is now at the Physics Department of Bielefeld University!

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

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

  Jacobi Identity in de Sitter Superalgebra

+ 1 like - 0 dislike
726 views

In the book "Supergravity" (by D. Freedman and A. Van Proeyen) they talk about why $\mathcal{N}=1$ de-sitter superalgebra is impossible to construct (Section 12.6.1).

Basically de-Sitter algebra is a modification of flat space symmetry algebra with: $[P_μ,P_ν]=−\frac{1}{4L^2}M_{μν}$

Then if we try to embed this into a superalgebra with say: $[P_μ,Q_α]=\frac{a}{4L}(γ_μQ)_α$ with arbitrary "a" we see that the Jacobi identity involving $[P_μ,P_ν,Q_α]$is not satisfied.

Whereas in the paper "Construction of the de Sitter supergravity"(arXiv:1602.01678v2) the authors say:

Super-dS algebras do exist for even $\mathcal{N}=1$ in 4 dimensions (and for other D ≤ 6).

Which implies that having an R symmetry, somehow makes the above problem go away. My question is, how does that work out? Any reference is welcome.

Note: I tried to read W. Nahm's paper in which he classifies all the SUSY algebras. But that paper just has the list of algebras. If there's a reference that tackles the above problem in detail, it would be really appreciated.

asked Apr 12, 2020 in Theoretical Physics by Ari (15 points) [ no revision ]
recategorized Apr 22, 2020 by Dilaton

arXiv:1602.01678v2 states $\mathcal{N}$ must be even.  In particular $\mathcal{N} \neq 1.$

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).
Please complete the anti-spam verification




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

Your rights
...