| 研究実績の概要 |
Over the course of this fiscal year I have worked on two projects. The first involves a duality between Chern-Simons theory and a free boson theory. Averaging over the parameters of the free boson theory reproduces the Chern Simons theory in one higher dimension. Together with collaborators at IPMU, we worked out the details of this duality in the case of an arbitrary free boson theory, which is defined in terms of an arbitrary lattice. The parameters of the theory are the transformations which leave the lattice invariant. We showed that the corresponding bulk Chern-Simons theory can be defined in terms of the quadratic form of the lattice, and demonstrated the equality of the partition functions between the two theories. This provides an interesting extension of the holographic dictionary in an exactly solvable case.
The second project is related to a concept in condensed matter physics known as many-body quantum scars. These are high-energy states which look different from the typical state, and are not approximately thermal. Together with Zhiboedov, we investigated a gravitational analog of these states in the context of the AdS/CFT correspondence. This involves gravitational orbits around a black hole. We computed the decay time of these orbits, and showed that they are very long-lived. We also computed the energy spectrum of these states using a Bohr-Sommerfeld quantisation formula and connected the spectrum to known results, and showed that these states are not approximately thermal. This provides a new realisation of many-body scars in the gravitational context.
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