A Free Field Representation of the Osp(2|2) current algebra at level k=-2, and Dirac Fermions in a random SU(2) gauge potential

Abstract

The Osp(2|2) current algebra at level k=-2 is known to describe the IR fixed point of 2D Dirac fermions, subject to a random SU(2) gauge potential. We show that this theory has a simple free-field representation in terms of a compact, and a non-compact free scalar field, as well as a free fermionic ghost, at c=-2. The fermionic twist fields are crucial for the construction. The logarithmic current-algebra primary field with vanishing scaling dimension, transforming in an indecomposable representation, appears as a consequence of familiar logarithmic operators at c=-2.

arXiv commentLaTeX

Cited by in corpus (11)

• Bits and Pieces in Logarithmic Conformal Field Theory
• On the SU(2|1) WZW model and its statistical mechanics applications
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• Holographic applications of logarithmic conformal field theories
• Disordered Systems and the Replica Method in AdS/CFT
• Operator Product Expansion in Logarithmic Conformal Field Theory
• Branes in the GL(1|1) WZNW-Model
• On the Percolation BCFT and the Crossing Probability of Watts
• Superspace conformal field theory
• Integrable quantum field theories with supergroup symmetries: the $OSP(1/2)$ case
• Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas