发表机构
Perimeter Institute for Theoretical Physics; ICTP South American Institute for Fundamental Research IFT-UNESP（Perimeter理论物理研究所; ICTP南美基础研究所 IFT-UNESP）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在ABJM理论中通过对角化反常维度矩阵，识别出16条偶然BPS算子轨迹，大N极限下与可积性一致，并揭示其黑洞类似性质及能隙差异。
AI 中文摘要
给定一个固定圈阶的超共形规范理论，BPS态可以通过两种方式研究——通过枚举幂零超荷的上同调类，或通过对反常维度矩阵进行对角化。第二种方式能更深入地了解全息理论如何根据算子是对偶于无视界几何还是黑洞来区分它们。为此，我们在以$N$为形式参数的$\mathrm{U}(N)_k \times \mathrm{U}(N)_{-k}$ ABJM理论中进行对角化。这使得定义算子的轨迹并关注那些仅在有限多个$N$值处为BPS的偶然算子成为可能。与$\mathcal{N}=4$超杨-米尔斯理论相比，在该理论中数值上难以研究多个这样的算子，而ABJM理论使我们能够访问16条这样的轨迹及其后代。我们展示了在大$N$极限下它们采取特别简单的形式，并与可积性预言一致。我们还展示了它们中的许多，如同黑洞一样，只能被特定类型的引力子所修饰，并评论了这一上同调练习对完整算子性质的影响。最后，我们展示了ABJM理论中第一个非BPS态的能隙在定性上以预期的方式不同于$\mathcal{N}=4$超杨-米尔斯理论。
英文摘要
Given a superconformal gauge theory at a fixed loop order, BPS states can be studied in two ways --- by enumerating cohomology classes of a nilpotent supercharge or by diagonalizing the anomalous dimension matrix. The second one allows for a deeper look at how holographic theories distinguish between operators based on whether they are dual to horizonless geometries or black holes. To this end, we carry out the diagonalization in $\mathrm{U}(N)_k \times \mathrm{U}(N)_{-k}$ ABJM theory with $N$ as a formal parameter. This makes it possible to define trajectories of operators and focus on the fortuitous ones which are characterized by being BPS at only finitely many values of $N$. In contrast to $\mathcal{N} = 4$ Super Yang-Mills, where it has been numerically prohibitive to study more than one of these, ABJM gives us access to 16 such trajectories along with their descendants. We show that they take an especially simple form at large $N$ where they agree with the predictions of integrability. We also show that many of them, as with black holes, can only be dressed by certain types of gravitons and comment on how this exercise in cohomology also has implications for properties of the full operators. Finally, we show that the gap to the first non-BPS state in ABJM theory qualitatively differs from that of $\mathcal{N} = 4$ Super Yang-Mills in the expected way.
Comments63 pages, 15 figures
