Composite Fermion Metals from Dyon Black Holes and S-Duality

TL;DR

This paper proposes a holographic duality between string theory in dyon black hole backgrounds and composite fermion metals, demonstrating matching thermodynamic and transport properties through S-duality, and providing evidence from black hole energy and fermion dynamics.

Contribution

It introduces a novel holographic duality linking dyon black holes to composite fermion metals, utilizing S-duality and Dirac quantization to explain magnetic flux attachment.

Findings

Black hole thermodynamics match composite fermion ground-state energy.

Transport properties exhibit Fermi liquid-like behavior.

Black hole and fermion dynamics show consistent cyclotron motion.

Abstract

We propose that string theory in the background of dyon black holes in four-dimensional anti-de Sitter spacetime is holographic dual to conformally invariant composite Dirac fermion metal. By utilizing S-duality map, we show that thermodynamic and transport properties of the black hole match with those of composite fermion metal, exhibiting Fermi liquid-like. Built upon Dirac-Schwinger-Zwanziger quantization condition, we argue that turning on magnetic charges to electric black hole along the orbit of Gamma(2) subgroup of SL(2,Z) is equivalent to attaching even unit of statistical flux quanta to constituent fermions. Being at metallic point, the statistical magnetic flux is interlocked to the background magnetic field. We find supporting evidences for proposed holographic duality from study of internal energy of black hole and probe bulk fermion motion in black hole background. They show good agreement with ground-state energy of composite fermion metal in Thomas-Fermi approximation and cyclotron motion of a constituent or composite fermion excitation near Fermi-point.