Advances in Theoretical and Mathematical Physics

The gl(1|1) super-current algebra: the rôle 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 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.

Article information

Source
Adv. Theor. Math. Phys., Volume 13, Number 1 (2009), 259-291.

Dates
First available in Project Euclid: 21 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1232551525

Mathematical Reviews number (MathSciNet)
MR2471858

Zentralblatt MATH identifier
1172.81016

Citation

LeClair , André. The gl(1|1) super-current algebra: the rôle of twist and logarithmic fields. Adv. Theor. Math. Phys. 13 (2009), no. 1, 259--291. https://projecteuclid.org/euclid.atmp/1232551525


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