超对称灰色星系、对偶修饰黑洞与超共形指数
Supersymmetric Grey Galaxies, Dual Dressed Black Holes and the Superconformal Index
AI总结：
本文基于灰色星系与对偶修饰黑洞解，提出 $\mathcal{N}=4$ Yang-Mills 超对称态大 $N$ 熵及超共形指数主导机制两项猜想，并得到与小 $N$ 数值结果定性一致的多相相图。
摘要：
受近期在 $AdS_5\times S^5$ 中构造灰色星系和 Dual Dressed Black Hole（对偶修饰黑洞）解的启发，我们提出两个关于 $\mathcal{N}=4$ Yang-Mills 理论中超对称态大 $N$ 熵的猜想。第一个猜想断言存在大量超对称态，这些态可被视为超对称黑洞与超对称“引力子”的非相互作用混合。它预言了一个包含十一个不同相的超对称态微正则相图，并对每一相中的超对称熵（作为5个电荷的函数）给出明确预言。超共形指数的微正则版本涉及在5参数电荷空间中一条线上对带有交替符号的态求和。我们的第二个（也更具试探性的）猜想断言，该求和由线上具有最大超对称熵的点主导。此猜想预言了超共形指数作为指标电荷函数的大 $N$ 公式，并预言了一个包含九个不同相的微正则指标相图。它预言超共形指数与黑洞熵在一个相中（即在一个电荷范围内）一致，而在其他相中（即在其他电荷取值下）不一致。我们将这些预言与 $N\leq10$ 时数值计算的超共形指数进行比较，发现定性一致。
英文摘要：
Motivated by the recent construction of grey galaxy and Dual Dressed Black Hole solutions in $AdS_5\times S^5$, we present two conjectures relating to the large $N$ entropy of supersymmetric states in ${\cal N}=4$ Yang-Mills theory. Our first conjecture asserts the existence of a large number of supersymmetric states which can be thought of as a non interacting mix of supersymmetric black holes and supersymmetric `gravitons'. It predicts a microcanonical phase diagram of supersymmetric states with eleven distinct phases, and makes a sharp prediction for the supersymmetric entropy (as a function of 5 charges) in each of these phases. The microcanonical version of the superconformal index involves a sum over states - with alternating signs - over a line in 5 parameter charge space. Our second (and more tentative) conjecture asserts that this sum is dominated by the point on the line that has the largest supersymmetric entropy. This conjecture predicts a large $N$ formula for the superconformal index as a function of indicial charges, and predicts a microcanonical indicial phase diagram with nine distinct phases. It predicts agreement between the superconformal index and black hole entropy in one phase (so over one range of charges), but disagreement in other phases (and so at other values of charges). We compare our predictions against numerically evaluated superconformal index at $N\leq10$, and find qualitative agreement.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
