Duality in strongly interacting systems: = 2 SUSY Yang-Mills and the quantum Hall effect

✍ Scribed by B.P. Dolan

• Book ID: 105357942
• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 591 KB
• Volume: 59
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/prop.201100055

✦ Synopsis

Abstract

Classical solutions of the vacuum Maxwell's equations exhibit a SO(2) duality symmetry, which is enhanced to Sl(2,R) when dilaton and axion fields are included. Quantum effects break this symmetry but semi‐classically Sl(2,Z) symmetry, or a sub‐group thereof, survives in Dirac‐Schwinger‐Zwanziger quantisation. Even this symmetry is expected to be broken in the full theory of quantum electrodynamics, but a modular sub‐group survives as an infinite discrete symmetry of the vacua of 𝒩 = 2 supersymmetric Yang‐Mills theory. An analogous situation occurs in the quantum Hall effect, where different quantum Hall states are related by a modular symmetry which is a sub‐group of Sl(2,Z). The similarities between the quantum Hall effect and supersymmetric Yang‐Mills are reviewed and a possible link via the gauge/gravity correspondence is described. Scaling exponents in the quantum Hall effect are derived using the gauge‐gravity correspondence.