Composite fermion metals from dyon black holes and S-duality

We propose that string theory in the background of quantized dyon black holes in four-dimensional anti-de Sitter spacetime is holographic dual to 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 behavior. Built upon Dirac-Schwinger-Zwanziger quantization condition, we propose that turning on magnetic charges to electric black hole along the orbit of Γ ₀(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 constituent or composite fermion excitations near the Fermi-point.