## Advances in Theoretical and Mathematical Physics

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

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

#### 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