$W_{\infty }$ algebra in the integer quantum Hall effects

Abstract

We investigate the $W_{\infty }$ algebra in the integer quantum Hall effects. Defining the simplest vacuum, the Dirac sea, we evaluate the central extension for this algebra. A new algebra which contains the central extension is called the $W_{1+\infty }$ algebra. We show that this $W_{1+\infty }$ algebra is an origin of the Kac-Moody algebra which determines the behavior of edge states of the system. We discuss the relation between the $W_{1+\infty }$ algebra and the incompressibility of the integer quantum Hall system.

23 pages, UT-671

References in corpus (2)

• Quasifinite highest weight modules over the Lie algebra of differential operators on the circle
• Algebraic Aspects of the Fractional Quantum Hall Effect

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• Spinor Field Realizations of the half-integer $W_{2,s}$ Strings
• Physical States and BRST Operators for Higher-spin $W$ Strings
• Explicit field realizations of W algebras