1305.0013 (Constantin Candu et al.)

The N=1 algebra W_\infty[μ] and its truncations    [PDF]

Constantin Candu, Carl Vollenweider

We construct and classify the most general classical and quantum N=1 W_\infty-algebras generated by the same spins as the singlet algebra of M fermions and M bosons in the vector representation of O(M) in the large M limit. This type of algebras appears in a recent N=1 version of the minimal model holography. Our analysis shows that there is a one parameter family W_\infty[\mu] of such algebras at every given central charge. We identify various truncations of W_\infty[\mu] with, on the one hand, (orbifolds of) the Drinfel'd-Sokolov reductions of the Lie superalgebras B(n,n), B(n-1,n), D(n,n) and D(n+1,n), and, on the other hand, (orbifolds of) three N=1 cosets. A closer inspection reveals that these cosets can be realized as a Drinfel'd-Sokolov reduction of B(n,n), D(n,n) and D(n+1,n). We then discuss the implications of our findings for the quantum version of the N=1 minimal model holography.

View original: http://arxiv.org/abs/1305.0013