2013 Fiscal Year Final Research Report
Study of String Theories from the viewpoint of rigidity
| Project/Area Number |
23654079
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | The University of Tokyo |
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Principal Investigator |
KATO Akishi 東京大学, 数理(科)学研究科(研究院), 准教授 (10211848)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 素粒子(理論) / 数理物理学 / 分配関数 / 不変量 / 変異 / 箙 / 弦理論 / 三角圏 |
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| Research Abstract |
One of the central issues of string theories is to understand "dualities". It is of crucial importance to study the generating functions of the stable states. In a joint work with Yuji Terashima (Tokyo Institute of Technology), we defined partition q-series for a quiver mutation loop (a loop in a quiver exchange graph in cluster algebra terminology). We showed that they enjoy various remarkable properties such as pentagon identities, relation with fermionic character formulas of certain conformal field theories, and modular properties. The partition q-series are defined solely in terms of combinatorial data and are independent of the details of the system under study. It is expected that the partition q-series proves to be a unifying framework for shedding new lights on dualities and quantization.
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