Abstract
Abstract
The Schur index of a 4 dimensional $$ \mathcal{N} $$
N
= 2 superconformal field theory counts (with sign) bosonic and fermionic states that preserve 4 supercharges. We consider the Schur indices of 4d $$ \mathcal{N} $$
N
= 4 super Yang-Mills and $$ \mathcal{N} $$
N
= 2 circular quiver gauge theories with gauge groups U(N) or SU(N). We calculate the exponentially dominant part of their asymptotic expansions as the index parameter q approaches any root of unity. We find that some of the indices exhibit “small” ($$ \mathcal{O} $$
O
(N0) as N → ∞) exponential growth, which is much smaller than an $$ \mathcal{O} $$
O
(N2) exponential growth of states that is indicative of a black hole. This implies that the indices do not capture a growth of states that would correspond to a supersymmetric black hole that preserves 4 supercharges in the holographic dual AdS theory. Interestingly, the exponentially dominant part in the Schur asymptotics we consider, depends on the parity of the rank N.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics