Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories

Abstract

We identify Moore-Read wavefunctions, describing non-abelian statistics in fractional quantum Hall systems, with the instanton partition of N=2 superconformal quiver gauge theories at suitable values of masses and Ω-background parameters. This is obtained by extending to rational conformal field theories the SU(2) gauge quiver/Liouville field theory duality recently found by Alday-Gaiotto-Tachikawa. A direct link between the Moore-Read Hall $n$-body wavefunctions and Z_n-equivariant Donaldson polynomials is pointed out.

Figures (4)

• Figure 1: A diagram representing the conformal block (\ref{['qh_cb']}). For the conformal block to be non zero, $n+N$ has to be even. For each diagram there are $n/2-1$ fields $X$ which can correspond to the $Id$ or to the $\sigma$ field, $X=\hbox{Id}$ or $X=\sigma$. The total number of possible conformal block is then $2^{n/2-1}$
• Figure 2: Diagram representing a ${\cal N}=2$ superconformal quivers. The circles corresponds to quiver nodes with $SU(2)$ gauge group. The boxes with two outgoing lines represent bifundamental matter and their $SU(2)$ global flavour symmetry. The linear quiver has two fundamental and two antifundamental hypermultiplets at the ends.
• Figure 3: Diagram representing the conformal block (\ref{['gencb']})
• Figure 4: Conformal blocks corresponding to the functions computed in Nayak_Wilczek