2020 Fiscal Year Research-status Report
Probing local gravitational physics with Lorentzian singularities in field
| Project/Area Number |
20K14465
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| Research Institution | The University of Tokyo |
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Principal Investigator |
DODELSON MATTHEW 東京大学, カブリ数物連携宇宙研究機構, 特任研究員 (40835617)
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| Project Period (FY) |
2020-04-01 – 2022-03-31
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| Keywords | String theory / Black holes / Chern-Simons theory / Conformal field theory |
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| Outline of Annual Research Achievements |
In the past fiscal year, I have made several important advances towards the goal of this program. First, I have published the paper "Singularities of thermal correlators at strong coupling" with Hirosi Ooguri. In this paper we analyzed singularities of correlation functions at finite temperature. These correlation functions can be computed using string theory near a black hole. The strings propagate outside the photon sphere of the black hole, and tidal effects can be analyzed exactly. We showed that the singularities are resolved if one takes these tidal effects into account. This paper was selected for an Editor's Suggestion prize by the Physical Review D journal.
Another direction in which I have made progress is on the connection between Chern-Simons theory and conformal field theory. Recently I have submitted the paper "Chern-Simons Invariants from Ensemble Averages," with M. Ashwinkumar,d A. Kidambi, J. Leedom, and M. Yamazaki. This paper matches the averaged partition function of a free boson theory with the partition function of Chern-Simons theory. Chern-Simons theory describes certain topological invariants of three dimensional spaces This paper connects to mathematical theorems discovered by Siegel almost a century ago.
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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
My work is proceeding as planned. I have published one paper and submitted another paper for publication over the past year, and I plan to release 1-2 more papers over the next few months, in order to complete this research program.
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| Strategy for Future Research Activity |
There are several directions in which we are currently investigating. First, with Ooguri, we are computing the interactions of strings near highly rotating black holes. The rotation acts as a particle accelerator, which may allow strings to be more easily detectible. Second, with Ashwinkumar, Kidambi, Leedom, and Yamazaki, we are computing correlation functions of twist operators in conformal field theory. This maps to certain invariants of vortices in Chern-Simons theory, which will lead to a further understanding of the ensemble average duality. Third, I am analyzing the singularities of correlation functions in certain two dimensional theories called nonlinear sigma models. There seem to be extra singularities from instantons that should not be there. I am attempting to resum these singularities to obtain a finite result. I hope to finish at least two of these directions in the next few months.
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| Causes of Carryover |
I have not used some of the grant money because it is difficult to travel due to COVID19. If travel becomes possible over the summer, I will use the money to travel. Otherwise, I will buy books and software that will be helpful for the project.
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