发表机构
Graduate School of Science, University of Tokyo; Kavli IPMU (WPI), UTIAS, The University of Tokyo; Center for Interdisciplinary Theoretical and Mathematical Sciences, RIKEN; Trans-Scale Quantum Science Institute, University of Tokyo（东京大学理学研究科; 理化学研究所 Kavli 宇宙物理数学统一研究所（WPI），东京大学理工学术研究院; 理化学研究所交叉理论科学中心; 东京大学跨尺度量子科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本书介绍3d-3d对应，以自下而上方式从量子场论基本问题出发，探讨三维N=2超对称理论与三维流形几何的联系，强调理论空间中显现的几何与代数结构。
AI 中文摘要
本书原为2015年由Saiensu-sha出版的日文著作，此为英文翻译版。本书是对3d-3d对应的导论，即三维N=2超对称规范理论与三维流形几何之间的关系，这种关系源于六维N=(2,0)理论的紧致化。本书采用自下而上而非自上而下的叙述方式：并非从六维理论出发，而是首先追问量子场论是什么，让几何自行显现。在叙述过程中，我们讨论了重整化与低能有效理论、作为将场论粘合在一起的操作的规范群化、由此产生的对三维理论的Sp(2n, Z)作用、三维N=2超对称理论及其对偶性、压扁的三球面配分函数与超对称局域化、四维N=2理论的对偶性畴壁、量子Teichmüller理论、复Chern-Simons理论以及三维流形上平坦SL(2, C)联络的模空间的量子化，并以量子双对数函数作为贯穿始终的主题。全书强调的重点是那些在单一场论中不可见、而仅在量子场论的理论空间中显现的几何与代数结构。附录总结了各维度的超对称性、经典与量子双对数函数以及簇代数。每章均包含附有难度评级的习题。
英文摘要
This is an English translation of a book originally published in Japanese by Saiensu-sha in 2015. The book is an introduction to the 3d-3d correspondence, the relation between 3d $\mathcal{N}=2$ supersymmetric gauge theories and the geometry of 3-manifolds, which arises from the compactification of the 6d $\mathcal{N}=(2,0)$ theory. The presentation is bottom-up rather than top-down: instead of starting from the 6d theory, we begin by asking what a quantum field theory is, and let the geometry emerge on its own. Along the way we discuss renormalization and low-energy effective theories, gauging as an operation which glues field theories together, the resulting $Sp(2n, \mathbb{Z})$-action on 3d theories, 3d $\mathcal{N}=2$ supersymmetric theories and their dualities, the squashed three-sphere partition function and supersymmetric localization, duality domain walls of 4d $\mathcal{N}=2$ theories, quantum Teichmuller theory, complex Chern-Simons theory and the quantization of the moduli space of flat $SL(2, \mathbb{C})$-connections on 3-manifolds, with quantum dilogarithm functions as a recurring thread. The emphasis throughout is on geometric and algebraic structures which are invisible in a single field theory, and appear only in the theory space of quantum field theories. Appendices summarize supersymmetry in various dimensions, classical and quantum dilogarithm functions, and cluster algebras. Exercises with difficulty ratings are included in each chapter.
Comments241 pages, 52 figures. English translation of a book published in Japanese by Saiensu-sha (SGC Library) in September 2015. Some typos and errors in the original have been corrected
