研究実績の概要 |
Developed an application of the effective field theory (EFT) construction techniques to a theory relevant for describing the canonical condensed matter Ising model - that is, phi4 theory in 4-epsilon dimensions. This involved understanding how the conformal structures that organise the operator basis impact the process of calculating quantum loop corrections, providing insight as to how the scattering elements can 'mix' into each other via these quantum effects. The 'asymptotic handle' to study the structure of EFT was further developed. This avenue was identified as a particularly useful one to gain insight into how redundancies remove operators from an EFT: that a direct (non asymptotic) approach is prohibitively hard can be understood by the mathematical connection to the study of partition functions. Indeed, there exists no closed-form expression for even the number of integer partitions; yet, the Ramanujan asymptotic formula gives an analytic handle. A more fine-grained approach was taken, to understand more detailed analytic properties of EFT operator bases in the asymptotic limit. The construction of EFTs is organized by symmetry. However one obstacle that was encountered in making contact with the literature was that often an organising symmetry is an outer-automorphism symmetry. These types of symmetry thus needed to be understood. This led to the observation that such symmetries could be anomalous - not preserved in the quantum theory (which is the theory of interest, including for dark matter scattering). These anomalies were investigated their nature elucidated.
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今後の研究の推進方策 |
Develop the elucidation of EFT with spontaneously broken symmetry. Acknowledge that there is an important class of theories that have not been systematically studied, namely when such a symmetry is gauged. These systems are prevalent in condensed matter, and thus are an important target for the goal of this project.
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