2013 Fiscal Year Final Research Report
W-constraints in Singularity Theory
| Project/Area Number |
23740005
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
MILANOV Todor 東京大学, カブリ数物連携宇宙研究機構, 特任助教 (80596841)
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| Project Period (FY) |
2011 – 2012
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| Keywords | エイナル－オランタン再帰関係式 / 周期積分 / フロベニウス構造 / 平坦構造 / 頂点代数 |
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| Research Abstract |
We constructed a vertex algebra representation via the period map in singularity theory that can be used to characterize the correlation functions of a certain class of Quantum Field Theories. In particular, the main goal of the proposal was achieved for simple singularities. The 2nd major achievement is the discovery that the correlation functions satisfy an Eynard-Orantin recursion. In particular, I managed to prove a conjecture of Givental about the analyticity of the total ancestor potential in singularity theory. Understanding the relation between the vertex algebra representation and the Eynard-Orantin recursion seems to be a very interesting problem that could bring a new insight on the representation theory of W-algebras.
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