$gl(2|2)$ Current Superalgebra and Non-unitary Conformal Field Theory

Abstract

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate $gl(2|2)$ current superalgebra at general level $k$. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented.

LaTex file 11 pages

References in corpus (3)

• Bits and Pieces in Logarithmic Conformal Field Theory
• Disordered Dirac Fermions: the Marriage of Three Different Approaches
• Twisted $sl(3,\mathbf{C}{)}_k^{(2)}$ Current Algebra: Free Field Representation and Screening Currents

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• Free field realization of the exceptional current superalgebra $\hat{D(2,1;\a)}_k$