About the notation OSP(8|4) etc.

  • Thread starter isospin
  • Start date
  • #1
14
0

Main Question or Discussion Point

Are there any books or papers which explain these notations like OSP(N|4), sl(m|n)? It seems they are all considered as superalgebras, but how is this kind notation generally defined?
By the way, I know for a 3-d superconformal field theory, OSP(8|4) means a SO(8) R-symmetry and a Sp(4) conformal symmetry, which is isomorphic to SO(2, 3).
Thanks.
 

Answers and Replies

  • #2
m|n denotes the number of bosonic (ordinary, even) dimensions and the number of fermionic (odd) dimensions. Thus, sl(m|n) is the special linear algebra acting on a superspace with m even and n odd dimensions. OSP stands for ortho-symplectic, because it mixes aspects of the orthogonal and symplectic groups. Recall that the orthogoal group preserves the even metric, and the symplectic group preserves the odd symplectic metric; the OSP group preserves a metric which symmetry depends on Grassmann parity.
 
  • #3
525
6
By any chance, do you know a good book or reference paper on these matters?
 
  • #4
Haelfix
Science Advisor
1,949
212
Try the book Supermanifolds by DeWitt
 

Related Threads for: About the notation OSP(8|4) etc.

Replies
5
Views
3K
Replies
0
Views
1K
Replies
20
Views
5K
Replies
4
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
22
Views
9K
  • Last Post
Replies
1
Views
2K
Replies
10
Views
5K
Top