Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-07-30
Commun.Math.Phys. 206 (1999) 493-531
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 37 pages
Scientific paper
Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras. We prove several general results on the ordering kernels associated to the adapted orderings and show that the size of an ordering kernel implies an upper limit for the dimension of a singular vector space. We apply this method to the topological N=2 algebra and obtain the maximal dimensions of the singular vector spaces in the topological Verma modules: 0, 1, 2 or 3 depending on the type of Verma module and the type of singular vector. As a consequence we prove the conjecture of Gato-Rivera and Rosado on the possible existing types of topological singular vectors (4 in chiral Verma modules and 29 in complete Verma modules). Interestingly, we have found two-dimensional spaces of singular vectors at level 1. Finally, by using the topological twists and the spectral flows, we also obtain the maximal dimensions of the singular vector spaces for the Neveu-Schwarz N=2 algebra (0, 1 or 2) and for the Ramond N=2 algebra (0, 1, 2 or 3).
Doerrzapf Matthias
Gato-Rivera Beatriz
No associations
LandOfFree
Singular dimensions of the N=2 superconformal algebras. I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Singular dimensions of the N=2 superconformal algebras. I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Singular dimensions of the N=2 superconformal algebras. I will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-112505