论文标题
4D Lagrangian理论的Schur指数的统一渐近学根源
Root of unity asymptotics for Schur indices of 4d Lagrangian theories
论文作者
论文摘要
$ 4 $ dimensional $ \ MATHCAL {n} = 2 $ SUPERCON -CON -CONSTORLIAN FIELD理论计数（带有符号）的玻感和费米子状态的Schur索引，可保留$ 4 $增压。我们考虑$ 4 $ d $ \ MATHCAL {n} = 4 $ SUPER YANG-MILLS和$ \ MATHCAL {N} = 2 $带有规格组$ U（N）$（N）$或$ SU（N）$的Schur索引。我们计算其渐近扩展的指数占主导地位，因为索引参数$ q $接近任何统一根。我们发现，某些索引表现出``小型''（$ \ Mathcal {o}（n^0）$作为$ n \ rightArrow \ infty $）指数增长，这要比$ \ nathcal {o}（o}（n^2）的状态的状态呈现为黑洞的状态的状态。有趣的是，全息双重广告理论中的4个增压。
The Schur index of a $4$ dimensional $\mathcal{N}=2$ superconformal field theory counts (with sign) bosonic and fermionic states that preserve $4$ supercharges. We consider the Schur indices of $4$d $\mathcal{N}=4$ super Yang-Mills and $\mathcal{N}=2$ 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" ($\mathcal{O}(N^0)$ as $N \rightarrow \infty$) exponential growth, which is much smaller than an $\mathcal{O}(N^2)$ 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 $N$.
