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arXiv · 0710.2906

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

André LeClair
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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 spin charge 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.

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André LeClair. 2007-10-16. The gl(1|1) super-current algebra: the role of twist and logarithmic fields. https://arxiv.org/abs/0710.2906

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