The 4d superconformal index near roots of unity and 3d Chern-Simons theory

  title={The 4d superconformal index near roots of unity and 3d Chern-Simons theory},
  author={Arash Arabi Ardehali and S. K. Narasimha Murthy},
  journal={Journal of High Energy Physics},
Abstract We consider the S3×S1 superconformal index ℐ(τ) of 4d $$ \mathcal{N} $$ N = 1 gauge theories. The Hamiltonian index is defined in a standard manner as the Witten index with a chemical potential τ coupled to a combination of angular momenta on S3 and the U(1) R-charge. We develop the all-order asymptotic expansion of the index as q = e2πiτ approaches a root of unity, i.e. as $$ \overset{\sim }{\tau } $$ τ ~ ≡ mτ+n → 0, with m, n relatively prime integers. The asymptotic… 
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