2019 Fiscal Year Annual Research Report
Digging deeper into effective field theory
| Project/Area Number |
18K13533
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Melia Thomas 東京大学, カブリ数物連携宇宙研究機構, 特任助教 (30814909)
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Keywords | Effective field theory / Operator bases |
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| Outline of Annual Research Achievements |
The goal of the project is to systematically construct operator bases - coordinate systems - for relativistic EFTs with linearly realized internal symmetries. The challenge is to account for redundancies between operators that fall into two categories: i) integration by parts (IBP), and ii) internal symmetry group relations.
IBP redundancies have been successfully and systematically accounted for, in line with the plan.
An operator basis modulo IBP takes the form of the harmonic modes of a Stiefel manifold (which is geometrically the collection of points obtained by rotating a coordinate frame about the origin). This has accomplished a novel take on EFT recasting it through the lens of harmonic analysis.
These harmonic modes are conformal primary operators, because the generalized Laplacian of the Stiefel manifold can be identified as the special conformal generator this makes the connection to the anticipated underlying conformal structure in EFT.
The identification of the Stiefel manifold has uncovered applications for Monte Carlo phase space generation. New applications of the techniques developed to theoretical aspects of dark matter direct detection were uncovered.
The research was disseminated in the form of publications in peer reviewed journals, and talks at international and domestic conferences.
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