S-duality constraints on 1D patterns associated with fractional quantum Hall states

Understand

Using the modular invariance of the torus, constraints on the 1D patterns are derived that are associated with various fractional quantum Hall ground states, e.g.

• through the thin torus limit.
• In the simplest case, these constraints enforce the well known odd-denominator rule, which is seen to be a necessary property of all 1D patterns associated to quantum Hall states with minimum torus degeneracy.
• However, the same constraints also have implications for the non-Abelian states possible within this framework.