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# Advances in Theoretical and Mathematical Physics

## Volume 13 (2009)

### Number 1

### The gl(1|1) super-current algebra: the rôle of twist and logarithmic fields

Pages: 259 – 291

DOI: https://dx.doi.org/10.4310/ATMP.2009.v13.n1.a8

#### Author

#### Abstract

A free field representation of the gl(1|1)_{k} current algebra at arbitrary level *k* is given in terms of two scalar fields and a symplectic fermion. The primary fields for all representations are explicitly constructed using the twist and logarithmic fields in the symplectic fermion sector. A closed operator algebra is described at integer level *k*. Using a new super spincharge separation involving gl(1|1)_{N} and su(*N*)_{0}, we describe how the gl(1|1)_{N} current algebra can describe a non-trivial critical point of disordered Dirac fermions. Local gl(1|1) invariant lagrangians are defined which generalize the Liouville and sine-Gordon theories. We apply these new tools to the spin quantum Hall transition and show that it can be described as a logarithmic perturbation of the osp(2|2)_{k} current algebra at *k* = −2.

Published 1 January 2009