| 研究課題/領域番号 |
26400242
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| 研究機関 | 東京大学 |
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研究代表者 |
HELLERMAN Simeon 東京大学, カブリ数物連携宇宙研究機構, 准教授 (70534949)
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| 研究期間 (年度) |
2014-04-01 – 2017-03-31
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| キーワード | conformal field theory / effective string theory / conformal bootstrap / mesons / confinement / O(2) model / strong coupling / nonperturbative |
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| 研究実績の概要 |
Our research plan for FY 2015 was to exploit our existing computational tools to fill out a systematic picture of generic constraints on CFT and on string theories and the connections between them, and to apply this information to questions of broad theoretical and phenomenological interest.
An area of great current interest is that of strongly coupled three dimensional conformal field theory, such as the three dimensional Ising model, on which stunning recent progress has been made by the application of analytic tools involving the conformal bootstrap. All known applications of the modern numerical bootstrap approach in D>=3, involve bounds on low-dimensional operators. Our parallel work in D=2, described above, has shown unambiguously that bootstrap methods can be applied in situations (large central charge for the partition function in D=2) that are analogous to large operator dimension in D>=3. In light of that, we have developed new techniques that apply specially to the case of high-dimension operators in D=3, which have dramatically improved and refined existing results coming from numerical bootstrap methods.
My collaborators and I have used these techniques to derive precise sum rules on operator dimensions that cannot be seen in the contextof a weakly coupled Lagrangian, and are also inaccessible in practice to numerical bootstrap techniques. Our results hint strongly at a complementarity or "duality" between Lagrangian and bootstrap techniques in strongly coupled 3D conformal field theory.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
We have progressed very well in our research plan!
(A) GOAL: Extend nonperturbative, model-independent constraints previously derived in 2D conformal field theory, to constrain strongly interacting conformal field theories in three dimensions: ACCOMPLISHED.
Though our results make some general assumptions about the theory (unitary, conformal, posessing an Abelian global symmetry, non-degenerate spectrum on flat spatial slices), they rely on no further specific information about the spectrum or interactions of conformal fields. Despite this, we have derived powerful constraints in the form of an asymptotic expansion for operator dimensions at large global charge, and related sum rules.
(B) GOAL: begin to apply the study of generic string theory to phenomenologically relevant situations, such as spacetimes holographically describing confining gauge theory through holographic duality: ACCOMPLISHED.
We have derived a preliminary proof of the "boundary dressing rule", which dictates the J-scaling of matrix elements of the boundary hamiltonian of the confining string of planar QCD, at large spin J. The proof can be understood from many points of view, but the most natural is by embedding the rotating string into a holographic gauge theory, and taking a limit in which the string is pinned to the bottom of its potential in the holographic direction. The boundary dressing rule has direct phenomenological consequences: It implies negative quarter-integer scaling laws appearing in sum rules for the spectrum and interactions of highly spinning mesons.
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| 今後の研究の推進方策 |
In FY2016 I am going to do the following:
1. Extend the general results on large operator dimension in 3D CFT (primarily the O(2) model) to the case of N=2 (and higher) supersymmetry, in which there is a moduli space of exactly supersymmetric, Lorentz-invariant vacua. In this class of models, the ideas of our work on high-dimension operators in the O(2) model have a natural generalization: The dynamics of high-dimension operators carrying R-charge, is encoded in the low-energy dynamics of moduli space, and subleading large-J corrections are encoded in higher-derivative terms in the moduli space effective action. We will also extend our work to four and higher dimensions.
2. Use quantum information-theoretic ideas to constrain conformal field theory in the quantum regime. In particular, we will investigate the connection of anomalies with the quantum-mechanical flow of information. Anomalies are very constraining on the dynamics of quantum field theory. Our initial results indicate a striking impact of nonvanishing anomaly matching coefficients (in 't Hooft's sense, of coefficients measuring the obstruction to gauging a global symmetry) on the definition of quantum information in a local quantum field theory.
3. Write a paper to explain the origin of the "boundary dressing rule" in the worldsheet theory of the effective QCD string at large angular momentum. Our initial results indicate that the boundary Hamiltonian of the effective string is comprised of operators whose matrix elements scale with negative quarter-integer powers of the angular momentum.
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| 次年度使用額が生じた理由 |
The reason for under-spending my grant by 45,352 JPY was that certain projects progressed more rapidly than originally projected, and as a result, overseas research visits were shorter than I could have anticipated initially. Also, my overseas collaborators were not able to visit during FY2016 as originally hoped, due to scheduling conflict.
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| 次年度使用額の使用計画 |
Though we were able to collaborate remotely and complete our project successfully, our collaboration will continue, and I plan to apply the carried-over balance to lengthen my research visit overseas and/or bring my collaborators to visit IPMU during FY2016.
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