Speaker: | T. Kobayashi (Hokkaido Univ.) | |
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Title | Deconstruction | |
E-Print |
[1] Y. Tatsuta, A. Tomiya,
"(De)Constructiong magnetized dimensions"
[arXiv:1703.05263[hep-th]] [2] G. F. Giudice, M. McCullough, "A Clockwork Theory" [arXiv:1610.07962[hep-ph]] |
Speaker: | ヤン ジャクリン (KEK)『ILCの物理と測定器』 高橋 徹 (Hiroshima Univ.) 『ILCの加速器と計画の概要』 | |
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Afternoon(13:30~) | ||
Abstract | 国際リニアコライダー(ILC)は次世代の電子陽電子衝突エネルギーフロンティア加速器として、世界中の研究者の国際協力のもと研究開発 ・設計が行われています。国際プロジェクトILCの日本国内誘致に向けた動きも加速しています。本セミナーでは、ILCで期待されるヒッグス粒子や トップクォークの研究と新粒子発見の可能性、最先端の超伝導加速技術を用いた加速器設計、およびILC計画を実現するための国内外の取り組みについて、 ILC計画に携わる若手研究者を含む講師陣が解説します。 |
Speaker: | Bum-Hoon Lee (Sogang Univ.) | |
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Title | Cosmology and Gravity with the Gauss-Bonnet term |
Speaker: | N. Kawamoto (Hokkaido Univ.) | |
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Title | The origin of the quaternion for Generalized Gauge Theory | |
Abstract | Generalization of Chern-Simons action into arbitrary dimensions was proposed in our old paper (N. K. and Watabiki 1991). The formulation was based on the graded Lie algebra framework with a introduction of quatermions. The origin of the quaternion was mysterious from those time. Recently we have understood the origin of the quaternion and due to this we can now formulate Lie algebra based formulation of Chern-Simons actions into arbitrary dimensions. I will explain the motivation and history of this formulation in jounal club style. | |
E-Print |
[1]
Alessandro D' Adda, Noboru Kawamoto, Naoki Shimode, Takuya Tsukioka, "Quaternion based generalization of Chern-Simons theories in arbitrary dimensions,"
[arXiv:1609.03712[hep-th]] |
Speaker: | R. Nakayama (Hokkaido Univ.) | |
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Title | On the construction of charged operators inside an eternal black hole | |
E-Print |
[1]
M. Guica and D. Jafferis, "On the construction of charged operators inside an eternal black hole,"
[arXiv:1511.05627[hep-th]] [2] W. Donnelly and S. B. Giddings, "Observables, gravitational dressing and obstructions to locality and subsystems," [arXiv:1607.01025[hep-th]] |
Speaker: | A. Ishibashi (Kindai Univ.) | |
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Title | BMS Supertranslations and Gravitational Memory | |
Abstract | The “memory effect” is the permanent displacement of test particles near infinity produced by radiation burst and is, in principle, a measurable effect. The memory effect has been an active topic of study, particularly with regard to the relationship between the memory, BMS asymptotic symmetry, and soft gravitons. In this talk I will show how BMS supertranslation characterizes the memory effect in 4-dimension, and why they vanish in higher dimensions, providing explicit calculations of linear perturbation in a simple example, as well as a general, nonlinear analysis. This talk is based on papers: arXiv:1612.03290, arXiv:1702.00095 | |
E-Print |
[1]
Stefan Hollands, Akihiro Ishibashi, Robert M. Wald, "BMS Supertranslations and Memory in Four and Higher Dimensions," arXiv:1612.03290[gr-qc]
[2] David Garfinkle, Stefan Hollands, Akihiro Ishibashi, Alexander Tolish, Robert M. Wald," The Memory Effect for Particle Scattering in Even Spacetime Dimensions," arXiv:1702.00095[gr-qc] |
Speaker: | T. Okazaki (National Taiwan University) | |
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Title | Implications of Conformal Symmetry in Quantum Mechanics | |
Abstract | In conformal quantum mechanics with the vacuum of a real scaling dimension and with a complete orthonormal set of energy eigenstates which is preferable under the unitary evolution, the dilatation expectation value between energy eigenstates monotonically decreases along the flow from the UV to the IR. In such conformal quantum mechanics there exist bounds on scaling dimensions of the primary operator and those of the gauge operator. | |
E-Print |
[1]
Ruth Britto-Pacumio, Jeremy Michelson, Andrew Strominger, Anastasia Volovich, "Lectures on Superconformal Quantum Mechanics and Multi-Black Hole Moduli Spaces," arXiv:hep-th/9911066
[2] Sergey Fedoruk, Evgeny Ivanov, Olaf Lechtenfeld, "Superconformal mechanics," arXiv:1112.1947[hep-th] [3] Tadashi Okazaki, "Superconformal Quantum Mechanics from M2-branes," arXiv:1503.03906[hep-th] [4] Tadashi Okazaki, "AdS2/CFT1, Whittaker vector and Wheeler-De Witt equation," arXiv:1510.04759[hep-th] [5] Tadashi Okazaki, "Implications of Conformal Symmetry in Quantum Mechanics," arXiv:1704.00286[hep-th] |
Speaker: | H. Maeda (Hokkai-Gakuen Univ.) | |
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(Morning session only) | ||
Title | Exact solutions with a scalar field in general relativity | |
Abstract | The recently found Higgs scalar field completes the standard model in particle physics. From the viewpoint of unified theory, scalar fields are natural since they arise naturally in supergravity or theories obtained through dimensional reduction to effective four-dimensional theories. For this reason, the Einstein-scalar-field systems with various potentials and/or couplings have been investigated to reveal the nature of gravity and the universe. In this talk, I present a variety of new (and known) exact solutions in general relativity with a nontrivial scalar field and seek with the audience their possible applications. | |
E-Print |
[1]
H. Maeda, Cristian Martinez, "All static and electrically charged solutions with Einstein base manifold of Einstein-Maxwell massless scalar field system in arbitrary dimensions," [arXiv:1603.03436 [gr-qc]]
[2] Hideki Maeda, "The Roberts–(A)dS spacetime" [arXiv:1501.03524 [gr-qc]] [3] Sourav Bhattacharya, Hideki Maeda, "Can a black hole with conformal scalar hair rotate?" [arXiv:1311.0087 [gr-qc]] [4] Hideki Maeda, "Exact dynamical AdS black holes and wormholes with a Klein-Gordon field" [arXiv:1204.4472 [gr-qc]] [5] Andres Anabalon, Hideki Maeda, "New Charged Black Holes with Conformal Scalar Hair" [arXiv:0907.0219 [hep-th]] [6] Hideki Maeda, "A Simple analytic model of wormhole formations" [arXiv:0811.2962 [gr-qc]] |
Speaker: | Natsumi Nagata (Univ. of Tokyo) | |
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Title | Searching for electroweak-charged dark matter | |
Abstract | The neutral component of an electroweak multiplet is a good candidate for dark matter in the Universe. In this talk, I will systematically list such dark matter candidates and review their phenomenological properties. Then, I will discuss how to probe such a dark matter candidate in direct detection experiments, indirect searches, and collider experiments. |
Speaker: | K. Watanabe (YITP) | |
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Title | AdS from Optimization of Path-Integrals in CFTs | |
Abstract | Recently emergent spaces from tensor network descriptions for quantum states have been investigated actively as a toy model of holography or AdS/CFT. In this seminar, we reformulate this conjectured connection to (continuous) tensor networks from the viewpoint of Euclidean path- integrals which is another description for quantum states. We discuss an "optimization" procedure of Euclidean path-integrals for wave functionals in CFTs. For a ground state in 2d CFT, the optimization gives a hyperbolic space or a time slice of AdS3. We discuss it for other states and other dimensions. Also we apply our optimization procedure to reduced density matrices and it reproduces entanglement wedges and holographic entanglement entropies. Our prescription suggests how to estimate a computational complexity in CFTs. | |
E-Print | [1] P. Caputa, N. Kundu, M. Miyaji, T. Takayanagi, K. Watanabe, "AdS from Optimization of Path-Integrals in CFTs", [arXiv:1703.00456[hep-th]] |
Speaker: | R. Takahashi (Tohoku Univ.) | |
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Title | Inflation models: Higgs inflation with singlets, Higgs inflation with a running kinetic term, and CW inflation | |
Abstract | Some inflation models are discussed after the review of inflation. The models are Higgs inflation with singlets (right-handed neutrinos and scalar dark matter), Higgs inflation with a running kinetic term, and CW inflation models. This talk is based on papers [1-4]. | |
Refferences |
[1] Naoyuki Haba, Ryo Takahashi, "Higgs inflation with singlet scalar dark matter and right-handed neutrino in light of BICEP2,"
Phys.Rev. D89 (2014) no.11, 115009,
arXiv:1404.4737[hep-ph]
[2] Naoyuki Haba, Hiroyuki Ishida, Ryo Takahashi, "Higgs inflation and Higgs portal dark matter with right-handed neutrinos," PTEP 2015 (2015) no.5, 053B01, arXiv:1405.5738[hep-ph] [3] Fuminobu Takahashi, Ryo Takahashi, "Renormalization Group Improved Higgs Inflation with a Running Kinetic Term," Phys.Lett. B760 (2016) 329-334, arXiv:1603.07601[hep-ph] [4] Kunio Kaneta, Osamu Seto, Ryo Takahashi, "Small inflation scale from realistic Coleman-Weinberg inflation," in preparation |
Speaker: | Johannes Braathen (LPTHE at Univ. Pierre and Marie Curie) | |
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(Afternoon session only) | ||
title | Generic two-loop Higgs mass calculations and the solution to the Goldstone boson catastrophe | |
Abstract | After the discovery of the Higgs boson, precision calculations of its properties are of great importance in the study of extensions of the Standard Model. The state-of-the-art calculation of Higgs masses is now at two-loop order for generic theories, performed in the Landau gauge. However, these calculations are plagued by infrared divergences due to tachyonic running Goldstone masses -- the so-called Goldstone boson catastrophe (GBC). This problem is present in the SM and many BSM models, but it is particularly grave for theories where the pseudoscalar contributions to the Higgs mass are large, which is typically the case for non-supersymmetric models. In a first introductory part, I will recall the theoretical tools used for Higgs mass calculations in the context of generic models and present some examples of their numerical implementation (among which the spectrum generator generator SARAH). Then I will show how the Goldstone boson catastrophe appears in these calculations and how it may be addressed. I will focus in particular on the recent solution to this problem in the context of general renormalisable field theories [1609.06977]. I will finish by illustrating the study of two-loop corrections to Higgs masses in non-supersymmetric models, made possible by the implementation of the solution to the GBC in SARAH. | |
E-Print | [1] Johannes Braathen, Mark D. Goodsell, "Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops," [arXiv:1609.06977[hep-th]] |
Speaker: | Y. Nishimura | |
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Title | TBA |
M2 Journal club | ||
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Morning | ||
Speaker: | K. Tanaka (Hokkaido Univ.) | |
Title | Yukawa coupling from superstring | |
Afternoon | ||
Speaker: | S. Nagamoto (Hokkaido Univ.) | |
Title | Toroidal compactification models of superstring |
M2 Journal club | ||
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Speaker: | K. Shiohara (Hokkaido Univ.) | |
Title | Bulk reconstruction based on AdS isometry |
Informal lecture | ||
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Speaker: | K. S. Choi (Ewha Womens University) | |
Title | A Tour on Calabi-Yau compactification | |
Abstract | We present a brief overview of compactification. Many problems of the Standard Model can be translated to the properties of extra dimensions, which arise naturally from string theory. We would like to look at some key ideas: Kaluza-Klein reduction, gauge flux, chirality and Calabi-Yau space. |
Speaker: | K. Yorita (Waseda University) | |
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Title | The latest results from ATLAS | |
Abstract | An overview of recent results in physics analyses obtained with the ATLAS experiment at the Large Hadron Collider located at CERN, is presented. The focus is on measurements of the Standard Model processes, properties of the recently discovered Higgs boson, as well as results of a wide variety of searches for physics beyond the Standard Model. And future prospects for precise measurements and physics searches at the ATLAS are also discussed. |
Speaker: | N. Omoto (Hokkaido University) | |
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Title | B decays | |
Abstract | S. Bifani for the LHCb Collaboration, Search for new physics with b->sll decays at LHCb, CERN Seminar, 18, April 2017, (https://cds.cern.ch/record/2260258), and more |
M2 Journal Club | ||
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Speaker: | I. Saga (Hokkaido University) | |
Title | New D-term Inflation | |
Rehearsal of M1 Journal Club | ||
Speaker: | Y. Ohie (Hokkaido University) | |
Title | N=2 Supersymmetric Gauge Theory and its Rigorous Solution |
Morning Session Only | ||
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Speaker: | Alessandro D'Adda (University of Turin) | |
Title | An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry | |
e-print | [1] Alessandro D'Adda, Noboru Kawamoto, and Jun Saito, "An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry", arXiv:1706.02615[hep-lat] |
Speaker: | T. Sasaki (Hokkaido University) | |
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Title | Asymptotic symmetries on black hole horizon | |
e-print |
[1] K. Sousa, G. Miláns del Bosch, and B. Reina,
"Supertranslations: redundancies of horizon data, and global symmetries at null infinity",
arXiv:1707.02971[hep-th] [2] Emil T. Akhmedov and Mahdi Godazgar, "Symmetries at the black hole horizon", arXiv:1707.05517[hep-th] [3] Rong-Gen Cai, Shan-Ming Ruan, and Yun-Long Zhang, "Horizon supertranslation and degenerate black hole solutions", arXiv:1609.01056[gr-qc] [4] Laura Donnay, Gaston Giribet, Hernán A. González, and Miguel Pino, "Extended symmetries at the black hole horizon", arXiv:1607.05703[hep-th] [5] Laura Donnay, Gaston Giribet, Hernán A. González, and Miguel Pino, "Supertranslations and Superrotations at the Black Hole Horizon", arXiv:1511.08687[hep-th] | |
Rehearsal of M1 Journal Club | ||
Speaker: | D. Sasaki (Hokkaido University) | |
Title | Conformal field theory and conformal bootstrap |
Morning | ||
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Speaker: | J. Yamamoto (Kyoto University) | |
Title | Poly-instanton axion inflation | |
Abstract | Superstring theory which is compactification by Calabi-Yau manifold has Kähler moduli including axions, that are related to deformations of extra dimension’s scale. Yet, in type IIB superstring theory this moduli field cannot be stabilized by α′ and string loop correction of tree level since the theory has quality called by ‘no-scale structure’. Generally, this Kähler moduli can be stabilized by non-perturbative correction, e.g. D-brane instanton. Then the axion potential that generated by the non-perturbative correction is represented by simple sin function. Compared to the individual non-perturbative correction as mentioned above, there are non-perturbative corrections among individual ones and they are called by ‘poly-instanton effects’. We discussed that in the case poly-instanton effect works sufficiently, axion has a potential which is different from simple sin function, and we evaluated how the potential can be generated. Then we saw that the potential is suited to inflation. In this talk, I will outline moduli of superstring theory, perturbative correction, non-perturbative correction and moduli stabilization, and after that I will describe axion inflation by poly-instanton effect, which is based on arXiv:1705.04088[hep-ph]. | |
Afternoon | ||
Speaker: | S. Uemura (Kyoto Sangyo University) | |
Title | Kähler moduli stabilization in semi-realistic magnetized orbifold models | |
Abstract | Moduli stabilization is one of the most important problems for string theory. In type IIB compactiﬁcations, 3-form ﬂuxes can stabilize the dilaton and complex structure moduli ﬁelds, but Kähler moduli remain massless. We study Kähler moduli stabilizations in semi-realistic magnetized D-brane models on Z_{2} × Z_{2}′ toroidal orbifolds. In this set up, the ratio of K¨ahler moduli is fixed by FI terms generated by magnetic fluxes on the D-branes, and the overall scale is stabilized non-perturbatively. We consider D-brane instanton eﬀects as the concrete non-perutrbative effect, and investigate the brane conﬁgurations to conﬁrm that the moduli ﬁelds can be stabilized successfully. This talk is based on arXiv:1703.03402[hep-th]. |
Speaker: | O. Morikawa (Kyushu University) | |
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Morning | ||
Title | Conformal field theory and the Landau-Ginzburg description | |
Abstract | I review some basic ingredients of the conformal field theory. In particular, I discuss its Landau--Ginzburg description, which is the main subject of the study presented in the afternoon talk. | |
Afternoon | ||
Title | Numerical study of \(\mathcal{N}=2\) Landau-Ginzburg models | |
Abstract | The two-dimensional \(\mathcal{N} = 2\) Wess--Zumino model is believed to provide the Landau--Ginzburg description of the superconformal field theory. This model is strongly coupled at IR, thus, it is difficult to prove this conjecture. To systems with some quasi-homogeneous superpotentials, we apply a SUSY-preserving numerical algorithm based on the Nicolai map. From the fitting of two-point functions in the low-energy region, we obtain the scaling dimension and the central charge, which are consistent with the conjecture. |
Intensive Lecture | ||
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Speaker: | S. Hosono (Gakushuin University) | |
Title | 物理学のための幾何学入門1・2 |
Seminar (Start at 16:00) | ||
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Speaker: | S. Hosono (Gakushuin University) | |
Title | 超弦理論とミラー対称性の世界 | |
Abstract | 超弦理論は10次元で定義されているが、6次元を非常に小さい多様体とすると、我々の4次元理論が実現することが知られている。 そして内部6次元空間はカラビヤオ多様体とすると超対称性を保った4次元理論とすることができる。カラビヤオ多様体には、 2次元的穴の数と3次元的穴の数が入れ替わった多様体が存在し、それらをミラー多様体と呼ぶ。このことから、物理学者たちは、 数学的には計算が困難であった、巻き付き数の数え上げ問題が単純な解析的問題として計算できるという予想を行った。 そしてその後それが数学者たちによって徐々に証明されてきたのである。 ここでは、これらミラー対称性の発見の経緯や最近までの研究成果を説明する。 | |
Rehearsal of M1 Journal Club | ||
Speaker: | S. Tamba (Hokkaido University) | |
Title | Yukawa couplings from Superstring Theory |
Speaker: | K. Aoki (Waseda University) | |
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Title | Massive Gravitons as Dark Matter | |
Abstract | The massive graviton has long received much attention from both theoretical and phenomenological aspects, ever since the linear theory of the massive spin-2 field was constructed by Fierz and Pauli in 1939. In this talk, after a brief introduction to the theories of the massive graviton, I discuss the possibility that the massive graviton is a viable candidate for dark matter mainly based on our recent papers arXiv: 1604.06704 and arXiv: 1707.05003. While the graviton is a mediator of the gravity, the graviton itself is a source of the gravitational field due to the nonlinearities of the field equation and then the massive graviton acts as dark matter. I provide two scenarios, particle dark matter scenario and field dark matter scenario, depending on the production mechanism. In both cases, future gravitational wave observations could play an important role to test the scenarios. | |
Rehearsal of M1 Journal Club | ||
Speaker: | T. Hasegawa (Hokkaido University) | |
Title | Chiral anomaly |
Speaker: | O. Seto (Hokkaido University) | |
---|---|---|
Title | DAMPE results and interpretations | |
e-print |
[1]
J. Chang et al, Astroparticle Physics 95, Pages 6-24, 2017
[2] DAMPE Collaboration, Nature 24475, 2017 [3] K. Fung and X.-J Bi, arXiv:1711.10996 [4] Q. Yuan et at, arXiv:1711.10989 + many others |
Speaker: | M. Suzuki (ICRR) | |
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Title | A "Gauged" U(1) Peccei-Quinn Symmetry | |
Abstract | The Peccei-Quinn (PQ) mechanism has been extensively studied as the most successful solution to the strong CP problem. In the PQ mechanism, a global U(1) symmetry (the PQ symmetry) is spontaneously broken leading to a pseudo Nambu-Goldstone boson, the axion. Through the axial anomaly of QCD, the axion obtains non-vanishing potential, and the effective θ-angle of QCD is cancelled by the vacuum expectation value (VEV) of the axion. Although the PQ mechanism is successful as it stands, the origin of the PQ symmetry is puzzling. First of all, the PQ symmetry is not an exact symmetry but an anomalous symmetry by definition. Besides, it is widely believed that physics at Planck scale does not respect global symmetries. Once the PQ symmetry is broken by the Planck suppressed operators, the PQ mechanism is easily ruined and does not solve the Strong CP problem. In this talk, after a brief introduction to the PQ mechanism and axion cosmology, I discuss a general solution to the above remaining Strong CP problem mainly based on our recent paper arXiv: 1703.01112. There, a global PQ symmetry is embedded into a gauge symmetry which is a linear combination of two (or more) PQ symmetries. This situation is analogous to the U(1)Y symmetry of the SM where the anomalies in the lepton sector are cancelled with ones in the quark sector. Furthermore, we comment the axion cosmology in this mechanism and apply this mechanism to the supersymmetric model. |
Speaker: | K. Suehiro (Hokkaido University) | |
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Title | Three-dimensional dualities with bosons and fermions | |
e-print | [1] F. Benini, Three-dimensional dualities with bosons and fermions |
Morning (Rehearsal of Master Thesis Presentation) | ||
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Speaker: | I. Saga (Hokkaido University) | |
Title | Modulus D-term Inflation | |
Afternoon (Seminar) | ||
Speaker: | K. S. Choi (Ewha Womans University) | |
Title | Global Consistency Condition in Heterotic M-theory | |
Abstract | Although chiral theory enjoys anomaly structure, consistent vacua with appropriate spectrum is free of anomalies. If we embed such theory in string theory, we automatically have anomaly free vacua if it is subject to global consistency condition. A well-known example is the modular invariance of the partition function of the heterotic string. In this talk, we introduce the elliptic genus, a modification of the partition function, to take into account the effect of M5-branes. |
Rehearsal of Master Thesis Presentation | ||
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Morning | ||
Speaker: | K. Shiohara (Hokkaido University) | |
Title | CFT representation of bulk localized states for fields with spin in AdS | |
Afternoon | ||
Speaker: | S. Nagamoto (Hokkaido University) | |
Title | Study of string phenomenology with modular transformation | |
e-print |
[1] T. Kobayashi, S. Nagamoto, and S. Uemura, arXiv:1608.06129[hep-th] [2] T. Kobayashi and S. Nagamoto, arXiv:1709.09784[hep-th] | |
Speaker: | K. Tanaka (Hokkaido University) | |
Title | Lepton mixing angles from flavor symmetries |
Short rehearsal of master thesis presentation | ||
---|---|---|
Speaker: | K. Shiohara (Hokkaido University) | |
Title | AdSバルクにおける局所的な場の状態のCFT表現 | |
Speaker: | I. Saga (Hokkaido University) | |
Title | 超対称性理論に基づくインフレーション模型の探求 | |
Speaker: | K. Tanaka (Hokkaido University) | |
Title | レプトン混合角を説明できるモジュラー対称性に由来する離散対称性を持つ理論模型の探索 | |
Speaker: | S. Nagamoto (Hokkaido University) | |
Title | モジュラー変換を用いた超弦理論の現象論に関する研究 |
Speaker: | T. Suzuki (Hokkaido University) | |
---|---|---|
Title | Holographic Entanglement of Purification | |
e-print |
[1]
T. Takayanagi, K. Umemoto, arXiv:1708.09393 [2] P. Nguyen, T. Devakul, M. G. Halbasch, M. P. Zaletel, and B. Swingle, arXiv:1709.07424 |
Speaker: | H. Suzuki (Hokkaido University) | |
---|---|---|
Title | Gauge Theory and Integrability | |
e-print |
[1]
K. Costello, E. Witten, and M. Yamazaki, arXiv:1802.01579 |
Speaker: | M. Sato (Hirosaki University) | |
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Title | 超弦幾何と弦理論の非摂動論的定式化 | |
Abstract | 弦幾何、つまり、相互作用を含めた超弦の集合、その位相、チャート、計量を定義する。 弦位相空間上の漸近的な軌跡の集合はターゲット多様体中の超リーマン面のモジュライを正しく再現する。 ゲージ場と結合するリーマン弦多様体上のアインシュタイン-ヒルベルト作用の経路積分によって、弦理論を非摂動論的に定式化する。 この理論は背景に依存しない。 理論は弦多様体上の一般座標変換対称性の一部として超対称性を持つ。 IIA, IIB, I型の摂動論的真空を表す背景を固定し、その周りの揺らぎから、IIA, IIB, I型それぞれの超弦の全オーダー摂動論的 散乱振幅を超モジュライを含めて導出する。 これらはただ一つの理論から導出される。また理論は、粒子だけでなく時空の点も、 ミクロに観測すると弦が観測されることを予言する。つまり、この理論は粒子と時空を統一する。 | |
e-print |
[1]
M. Sato, arXiv:1709.03506 |