  Using the renormalisation group (RG) we study two dimensional electromagnetic
coulomb gas and extended Sine-Gordon theories invariant under the modular group
SL(2,Z). The flow diagram is established from the scaling equations, and we
derive the critical behaviour at the various transition points of the diagram.
Following proposal for a SL(2,Z) duality between different quantum Hall fluids,
we discuss the analogy between this flow and the global quantum Hall phase
diagram.
