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Verma Modules, Extremal Vectors, and Singular Vectors on the Non-Critical N=2 String Worldsheet by Semikhatov, A. M. is a scholarly article available to read on EtoBox.

What is Verma Modules, Extremal Vectors, and Singular Vectors on the Non-Critical N=2 String Worldsheet about?

We formulate the general construction for singular vectors in Verma modules of the affine sl(2|1) superalgebra. We then construct sl(2|1) representations out of the fields of the non-critical N=2 string. This allows us to extend naturally to sl(2|1) several crucial properties of the N=2 superconformal algebra, first of all the construction of extremal states (an analogue of different pictures for non-free fermions) and the spectral flow transform (which then affects the Liouville sector). We further evaluate the affine sl(2|1) singular vectors in the realization of sl(2|1) provided by the N=2 string. We establish that, with a notable exception, the respective singular vectors are in a 2:1 correspondence, namely two different sl(2|1) singular vectors evaluate as an N=2 superconformal singular vector (however, those singular vectors that are labelled by a pair of positive integers get these integers transposed under the reduction). We also analyse the `exceptional' cases, which amount to a series of sl(2|1) singular vectors, labelled by r>=1, which do not have an N=2 counterpart, and discuss the mechanism by which the multiplicity of singular vectors becomes equal to two at certain p

Author

Semikhatov, A. M.

Published

1996

Language

EN