Conformal field theory of the integer quantum Hall plateau transition

Abstract

A solution to the long-standing problem of identifying the conformal field theory governing the transition between quantized Hall plateaus of a disordered noninteracting 2d electron gas, is proposed. The theory is a nonlinear sigma model with a Wess-Zumino-Novikov-Witten term, and fields taking values in a Riemannian symmetric superspace based on H^3 x S^3. Essentially the same conformal field theory appeared in very recent work on string propagation in AdS_3 backgrounds. We explain how the proposed theory manages to obey a number of tight constraints, two of which are constancy of the partition function and noncriticality of the local density of states. An unexpected feature is the existence of a truly marginal deformation, restricting the extent to which universality can hold in critical quantum Hall systems. The marginal coupling is fixed by matching the short-distance singularity of the conductance between two interior contacts to the classical conductivity sigma_xx = 1/2 of the Chalker-Coddington network model. For this value, perturbation theory predicts a critical exponent 2/pi for the typical point-contact conductance, in agreement with numerical simulations. The irrational exponent is tolerated by the fact that the symmetry algebra of the field theory is Virasoro but not affine Lie algebraic.

arXiv commentLateX, 63 pages, several points clarified, references added

References in corpus (10)

• More Comments on String Theory on AdS_3
• $PSL(n|n)$ Sigma Model as a Conformal Field Theory
• Point-Contact Conductances at the Quantum Hall Transition
• c-Theorem for Disordered Systems
• The Chalker-Coddington Network Model is Quantum Critical
• Another critique of the replica trick
• Information about the Integer Quantum Hall Transition Extracted from the Autocorrelation Function of Spectral Determinants
• Reflection Symmetry and Quantized Hall Resistivity near Quantum Hall Transition
• The color-flavor transformation and a new approach to quantum chaotic maps
• Gauge Invariance and the Critical Properties of Quantum Hall Plateaux Transitions

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• Representation theory of sl(2|1)
• Indecomposability parameters in chiral Logarithmic Conformal Field Theory
• Conformal Sigma-Models on Supercoset Targets
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• A modular invariant bulk theory for the c=0 triplet model
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• Boundary Spectra in Superspace Sigma-Models
• The Sigma Model on Complex Projective Superspaces
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• Conformal Current Algebra in Two Dimensions
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• Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model
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• Twenty-five years of two-dimensional rational conformal field theory
• A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part I: Algebraic structures in the spin chain. The Brauer algebra
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• Anomalous Dimensions in Deformed WZW Models on Supergroups
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• Logarithmic Correlations in Quantum Hall Plateau Transitions
• Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)
• A staggered six-vertex model with non-compact continuum limit
• Winding modes and the reflection symmetry in AdS${}_3$