发表机构
New York University; Virginia Tech（纽约大学; 弗吉尼亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出从GLSM库仑分支解释量子椭圆上同调环，以超势临界轨迹生成环关系，并处理四维规范反常阻碍，提供经典超势方案及对gerbes的预测。
AI 中文摘要
本文简要概述了一个关于量子椭圆上同调环的GLSM库仑分支解释的提议，该环目前在数学领域由Bouaziz-Huq-Kuruvilla-Lee发展。该提议以Fano环面簇的量子上同调和量子K理论的既定GLSM计算为模型，其中环关系表现为扭曲有效超势的临界轨迹。对于量子椭圆上同调，自然的推广将是将环关系编码在由四维理论经KK约化得到的二维理论的库仑分支计算中，描述平行表面缺陷的算子乘积展开，我们对此进行了回顾。然而，在一些基本例子中，这种解释受到四维规范反常的阻碍。在这种情况下，我们提供了一个经典超势，其临界轨迹生成预期的环关系，但该超势并非通过四维的KK约化获得，尽管它与这类KK约化共享许多特征。我们描述了一些简单例子，并对gerbes的情况做出了一些预测。
英文摘要
This paper briefly outlines a proposal for a GLSM Coulomb-branch interpretation of the quantum elliptic cohomology rings currently being developed in mathematics by Bouaziz-Huq-Kuruvilla-Lee. The proposal is modeled on the established GLSM computations of quantum cohomology and quantum K theory of Fano toric varieties, where ring relations arise as critical loci of twisted effective superpotentials. In the case of quantum elliptic cohomology, the natural generalization would be to encode ring relations in Coulomb branch computations in two-dimensional theories obtained by KK reductions from four-dimensional theories, describing OPEs of parallel surface defects, which we review. However, in some basic examples, this interpretation is obstructed by four-dimensional gauge anomalies. In such cases, we provide a classical superpotential whose critical loci generate the expected ring relations, but which is not obtained by KK reduction from four dimensions, though it shares many characteristics with such KK reductions. We describe some simple examples, and make some predictions for the case of gerbes.
Comments22 pages, LaTeX
