2023 Fiscal Year Research-status Report
Quantum fields and random geometries
| Project/Area Number |
21K20340
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| Research Institution | Okinawa Institute of Science and Technology Graduate University |
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Principal Investigator |
DELPORTE Nicolas 沖縄科学技術大学院大学, 重力、量子幾何と場の理論ユニット, ポストドクトラルスカラー (30913199)
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| Project Period (FY) |
2021-08-30 – 2025-03-31
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| Keywords | dirac walk / trees / outlier / random tensors |
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| Outline of Annual Research Achievements |
1. In arXiv:2312.10881 (accepted in JPhysA), we have concluded our work on Dirac walks, that generalize the random walks adapted to scalar fields to Grassmann variables, where the walk goes from vertex to edge and edge to vertex, on regular trees. Through recursive equations that are exactly solvable in the case of trees, we obtain explicit expressions for two-point functions between any two sites (vertex or edge) of the graph and compute the associated spectral dimension, identical to that of scalar random walks.
2. In arxiv:2405.07731, we have studied the eigenvalue spectrum of order 3 random tensors with deviation and found a phase transition as the variance of the noise increases that leads to the emergence and merging of an outlier of the spectrum.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The PhD student under our supervision has started to get more comfortable with the literature and tools, and we have a good collaboration ongoing with a professor of the YITP (Kyoto U).
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| Strategy for Future Research Activity |
1. We are setting up a study of the renormalization group flow of scalar fields on random locally tree-like graphs, using the formalism of FRG, using the spectral representation of the heat-kernel on the graph. We hope that this could later be generalized to more general graphs with loops.
2. We are looking at the spectrum of random tensors with more constrains such that can serve as the adjacency matrix of hypergraphs and hopefully return to the first point. The problem of the large order, as well as the distribution of complex eigenvalues, relevant in quantum information.
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| Causes of Carryover |
The remaining grant will be used for travels before fall between Okinawa and Kyoto where our main collaborators, Naoki Sasakura and Benoit Collins, work (that will be enough for one journey for each of us), or potentially for the last publication fee.
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