Lowest Landau Level Theory of Composite Fermi Liquid for SU(2) boson at total filling 1

We microscopically derived an effective field theory for composite fermi liquid(CFL) in lowest landau level for SU(2) boson at total filling 1 by generalizing N.Read's initial approach for spinless boson. In our theory,the Girvin-MacDonald-Platzman (GMP) algebra is satisfied exactly to all orders. At low energy(close to fermi surface), the effective field theory has two fermi surfaces coupled to one emergent U(1) gauge field without self chern simons term. In addition, each fermi surface has a Pi berry phase. As a result, the low energy theory can be UV completed to QED3 with two dirac fermions. Similar to Son's dirac theory for fermionic half-filled landau level CFL, physical density here is also carried by emergent flux.