捷克科学院物理研究所Paolo Rossi研究了奇异空间上B型超柔量力学的索引与定位。2025年4月24日出版的《高能物理杂志》发表了这项成果。

B型超量子力学σ模型在描述形成AdS2喉部的D-膜束缚态时具有物理意义。在这项工作中，研究组讨论了定位方法在这些理论中计算超共形指数的适用性，尽管它们的目标空间通常是奇异的。与最近关于A型模型的工作在精神上类似，他们建议在适当解析的目标空间上工作，以计算正则化索引。 

虽然这种正则化指数在物理感兴趣的模型中准确地捕捉到了实际指数，但研究组确实在更多的病理示例中发现了微妙之处。这发生在增压基本上不是自伴的情况下，在这种情况下，索引变得模糊，取决于所选的自伴扩展。研究组还讨论了具有Kähler目标空间的特殊类模型，它可以容纳A型和B型模型，并表明B型索引是A型索引的一个特定极限。对于Calabi-You锥，B型指数与未解空间的Hilbert级数一致。

附：英文原文

Title: Index and localization for type B superconformal mechanics on singular spaces

Author: Raeymaekers, Joris, Rossi, Paolo, anl, Canberk

Issue&Volume: 2025-04-24

Abstract: Type B superconformal quantum mechanical sigma models are of physical interest as they arise in the description of D-brane bound states forming an AdS2 throat. In this work we discuss the applicability of localization methods to compute the superconformal index in these theories, despite the fact that their target spaces are generically singular. Similar in spirit to recent works on type A models, we propose to work on a suitably resolved target space to compute a regularized index. While this regularized index correctly captures the actual index unambiguously in models of physical interest, we do uncover a subtlety in more pathological examples. This occurs in situations where the supercharge is not essentially-selfadjoint, in which case the index becomes ambiguous and depends on the chosen selfadjoint extension. We also discuss the special class of models with Khler target spaces, which can accommodate both type A and type B models, and show that the type B index is a particular limit of the type A index. For Calabi-Yau cones, the type B index coincides with the Hilbert series of the unresolved space.

DOI: 10.1007/JHEP04(2025)199

Source: https://link.springer.com/article/10.1007/JHEP04(2025)199