Quantum mirror map for del Pezzo geometries
Quantum mirror map for del Pezzo geometries
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DOI：
10.1088/1751-8121/ab93fe
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发表时间：
2019-08
期刊：
影响因子：
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通讯作者：
Tomohiro Furukawa;Sanefumi Moriyama;Yuji Sugimoto
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文献类型：
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作者：
Tomohiro Furukawa;Sanefumi Moriyama;Yuji Sugimoto
镜像映射在研究超对称规范理论中起着重要的作用。在这些理论中，动力学通常被编码成一条代数曲线，其中两组周期具有辛结构。A周期有助于重新定义被称为镜像映射的化学势。利用具有D5 Weyl群对称性的D5 del Pezzo几何的量子化，我们能够清楚地识别镜像映射的群论结构和多重覆盖结构。有了这些结构，我们可以将镜像映射应用到描述不同背景下多个M2膜的世界体积的超共形Chern-Simons理论中，我们发现化学势的重新定义是直接从镜像映射得到的。此外，我们还对镜像映射进行了有趣的观察：量子镜像映射中出现的表示与BPS指数中出现的表示相同，除了次数为1的微不足道的情况外，系数都是整数。
Mirror maps play an important role in studying supersymmetric gauge theories. In these theories the dynamics is often encoded in an algebraic curve where two sets of periods enjoy the symplectic structure. The A-periods contribute to redefinitions of chemical potentials known as mirror maps. Using the quantization of the D5 del Pezzo geometry, which enjoys the symmetry of the D5 Weyl group, we are able to identify clearly the group-theoretical structure and the multi-covering structure for the mirror map. With the structures, we can apply the mirror map to superconformal Chern–Simons theories describing the worldvolume of multiple M2-branes on various backgrounds, where we find that the redefinition of the chemical potential is obtained directly from the mirror map. Besides, we have interesting observations for the mirror map: the representations appearing in the quantum mirror map are the same as those appearing in the BPS indices except for the trivial case of degree 1 and the coefficients are all integers.