论文标题
$ \ frac {1} {16} $ - bps index in 4d $ \ mathcal {n} = 4 $ sym的增长
The growth of the $\frac{1}{16}$-BPS index in 4d $\mathcal{N}=4$ SYM
论文作者
论文摘要
我们研究了$ \ frac {1} {1} {16} $ - bps运算符的Hamiltonian索引中的4D $ \ Mathcal {n} = 4 $ u（n）super yang-mills（sym）理论在数值上，$ n = 2 \ \ ,, \ dots，10 $。我们表明，大电荷的渐近学与基于偶然的限制中的分析结果一致，这与双ADS中超对称黑洞的熵一致。数字也与大N分析结果一致，从而为指数提供了精确公式的提示。然后，我们使用表示理论的思想证明，对于小于2（n+1）的电荷值（以整数单位进行量化），该索引与多格拉维顿指数完全一致，然后开始偏离更大的电荷。因此，U（n）Sym索引在小电荷下的多graviton值与大电荷下的黑洞生长之间进行了插值。
We study the Hamiltonian index of $\frac{1}{16}$-BPS operators in 4d $\mathcal{N}=4$ U(N) super Yang-Mills (SYM) theory numerically for $N=2\,,\dots,10$. We show that the large-charge asymptotics agree with analytic results in the Cardy-like limit, as consistent with the entropy of supersymmetric black hole in the dual AdS. The numerics also agree with the large-N analytic result, thus providing hints towards an exact formula for the index. We then prove, using ideas from representation theory, that for values of charges (quantized in integer units) less than 2(N+1) the index agrees precisely with the multi-graviton index, and then begins to deviate for larger charges. Thus the U(N) SYM index interpolates between multi-graviton values at small charge and black hole growth at large charges.
