# 次回のセミナー (Next Seminar)

## The memory effect of Entanglement in 2D CFTs

When: 2019/06/24 (Mon.) 16:00-18:00 Honkan (Main Bldg.) H2-39 Song He (Jilin University, Professor) We will talk about the memory effect of entanglement entropy of locally excited states in two-dimensional conformal field theories (CFTs). In particular, we consider excited states obtained by acting on a vacuum with primary operators. We show that the entanglement entropy increases by a finite constant amount under its time evolution. Moreover, in rational conformal field theories, we prove that this increase of the (both Renyi and von Neumann) entanglement entropy always coincides with the log of the quantum dimension of the primary operator. Further, we also show the behavior of the time evolution of Entanglement in 2D quantum gravity and WCFTs. If the time is allowed, we will talk about the recent progress on this object in various deformed field theory.

# 最近のセミナー (Recent Seminars)

## TBA

When: 2019/07/24 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Takuya Okuda (Univ. of Tokyo, Komaba)

## TBA

When: 2019/07/17 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Toshihiro Ota (RIKEN) arXiv:1903.04718

## TBA

When: 2019/07/10 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Kanato Goto (RIKEN) TBA

## TBA

When: 2019/07/03 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Takahiro Uetoko (Ritsumeikan univ.)

## The memory effect of Entanglement in 2D CFTs

When: 2019/06/24 (Mon.) 16:00-18:00 Honkan (Main Bldg.) H2-39 Song He (Jilin University, Professor) We will talk about the memory effect of entanglement entropy of locally excited states in two-dimensional conformal field theories (CFTs). In particular, we consider excited states obtained by acting on a vacuum with primary operators. We show that the entanglement entropy increases by a finite constant amount under its time evolution. Moreover, in rational conformal field theories, we prove that this increase of the (both Renyi and von Neumann) entanglement entropy always coincides with the log of the quantum dimension of the primary operator. Further, we also show the behavior of the time evolution of Entanglement in 2D quantum gravity and WCFTs. If the time is allowed, we will talk about the recent progress on this object in various deformed field theory.

## Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries

When: 2019/06/19 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Noriyuki Sogabe (Keio university) In massless QCD coupled to QED in an external magnetic field, a photon with the linear polarization in the direction of the external magnetic field mixes with the charge neutral pion through the triangle anomaly, leading to one gapless mode with the quadratic dispersion relation $ω$∼$k^2$ and one gapped mode. In this talk, we show that this gapless mode can be interpreted as the so-called type-B Nambu-Goldstone (NG) mode associated with the spontaneous breaking of generalized global symmetries and that its presence is solely dictated by the anomalous commutator in the symmetry algebra. We also argue a possible realization of such nonrelativistic NG modes in $3$-dimensional Dirac semimetals. arXiv:1903.02846

## データ解析の数学的手法が描く正準テンソル模型の時空概念

When: 2019/06/10 (Mon.) 13:30-14:30 Honkan (Main Bldg.) H2-39 Naoki Sasakura (YITP)

## Deep learning & holographic QCD

When: 2019/05/29 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Akinori Tanaka (Riken) There is no doubt about that the deep learning (DL) is the one of the recent epoch-making achievement of the science. Recently, there are some movements in scientific community to apply DL or machine learning techniques to study their research fields. Even particle physics and string theory are not out of that movements. In this talk, I will review the concept of DL and our proposal to apply it to find gravity dual of given field theory. After that, I talk on our recent application in the context of holographic QCD. Physical Review D, 98(4), 046019.(arXiv:1802.08313) Physical Review D, 98(10), 106014.(arXiv:1809.10536)

## Super instanton counting and localization

When: 2019/05/08 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Taro Kimura (Keio university) We study the super instanton solution in the gauge theory with $U(n_+|n_−)$ gauge group. Based on the ADHM construction generalized to the supergroup theory, we derive the instanton partition function from the super instanton moduli space through the equivariant localization. We derive the Seiberg–Witten geometry and its quantization for the supergroup gauge theory from the instanton partition function, and study the connection with classical and quantum integrable systems. We also argue the brane realization of the supergroup quiver gauge theory, and possible connection to the non-supergroup quiver gauge theories. arXiv:1905.01513

## Anomaly, regularization and partition function on lens space

When: 2019/04/24 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Shuichi Yokoyama (YITP) In this talk, I will speak about how to derive a correct phase factor in partition function of N=2 SUSY gauge theory on three-manifold using three-sphere and lens space. In particular we reproduce a holonomy dependent phase factor associated Chern-Simons term derived by Imamura-Matsuno-Yokoyama from a fermion 1-loop determinant of regularization ghost for a vector multiplet. Our result improves their work on lens space partition function, and passes a couple of duality tests including the total phase.

## Correlation Functions on the 1/2-BPS Wilson Loop: Perturbation and Integrability

When: 2019/02/22 (Fri.) 13:30-15:00 Honkan (Main Bldg.) H2-39 Naoki Kiryu (Tokyo U., Komaba ) We study correlation functions of local operators inserted on the 1/2-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory in four dimensions. This is consistent with a holographic description of the correlators of open strings attached to D-branes in AdS5×S5. We first conjecture the finite coupling expression of the correlators in view of the integrability-based approach called “hexagonalization”, which was introduced previously to study the correlation functions in the absence of the Wilson loop. We next perform direct perturbative computation. Through the comparison with “hexagonalization”, we refine the conjecture for the integrability-based approach to the correlators on the 1/2-BPS Wilson loop. arXiv:1706.02989, arXiv:1710.07325, arXiv:1812.04593.

## 4次元N=2超共形場理論におけるBPSセクターにおけるOPE selection ruleの決定

When: 2019/01/30 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Kazuki Kiyoshige (大阪市立大学) Argyres-Douglas型の超共形場理論(SCFT)を始め、4次元N=2にはラグランジアンがないとされる非自明なSCFTが多数存在する。これらの理論の解析は演算子積展開(OPE)やindexなどの手法で行うことが主流になる。そこで我々は超共形代数の性質から決まるBPS条件を用いてOPE　selection rule を決定した。本研究では、(S)CFTにおいて特に重要なstress tensor と2d chiral algebra と関連のあるSchur 多重項と呼ばれるBPSセクターについてのselection rule (stress tensor × Schur multiplet)に絞って解析を行った。またそれらのselection rule から一般的な性質を予想した。 このトークはarXiv:1812.06394 [hep-th](西中氏との共同研究)に基づく。 arXiv:1812.06394

## Monodromifold planes: Refining $[p,q]$-branes and orientifold planes in string theory

When: 2019/01/23 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Naoto Kan (SOKENDAI) F-theory is the non-perturbative compactification of type IIB superstring theory. The compact space of F-theory has the structure of elliptic fibrations, which describe the compactification of type IIB string with the 7-branes background. The elliptic fibration is written by the Weierstrass form. In particular when we choose the base space as $\mathbb{P}^1$, then the whole of the compact space become the rational elliptic surface (RES) or the K3 surface. Furthermore, the discriminant loci of the Weierstrass form correspond to the D7-branes. On the other hand, the singularities of such a RES or K3 surface is classified by Kodaira, and B-branes and C-branes (or $[p,q]$-brane in general) with a monodromy emerge at singular points. The origin of such a monodromy can be thought of as f- and g-locus planes (named monodromifold planes) in the Weierstrass form. In this talk, I will start with the review of type IIB superstring theory and F-theory compactification and discuss the properties of monodromifold planes. Shin Fukuchi, Naoto Kan, Shun'ya Mizoguchi and Hitomi Tashiro, "Monodromifold planes: Refining (p,q)-branes and orientifold planes in string theory," arXiv:1808.04135

## Spinning conformal defects

When: 2018/12/07 (Fri.) 13:30-14:30 Honkan (Main Bldg.) H2-39 Nozomu Kobayashi (Kavli IPMU) We consider conformal defects with spins under the rotation group acting on the transverse directions. They are described in the embedding space formalism in a similar manner to spinning local operators, and their correlation functions with bulk and defect local operators are determined by the conformal symmetry. The operator product expansion (OPE) structure of spinning conformal defects is examined by decomposing it into the spinning defect OPE block that packages all the contribution from a conformal multiplet. The integral representation of the block derived in the shadow formalism is facilitated to deduce recursion relations for correlation functions of two spinning conformal defects. In simple cases, we construct spinning defect correlators by acting differential operators recursively on scalar defect correlators. arXiv:1805.05967 [hep-th]

## Holographic Entanglement of Purification and its Multipartite generalization

When: 2018/11/28 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Koji Umemoto (YITP) Recently it has been argued that there are deep connections between quantum gravity and quantum information theory, especially in the context of the AdS/CFT correspondence. In this talk we propose that so-called entanglement of purification, a generalization of entanglement entropy defined in boundary field theory, has a clear geometrical counterpart represented by the minimal area of certain codimension-2 surfaces (entanglement wedge cross-section) in dual bulk gravity. This proposal can be regarded as a generalization of Ryu-Takayanagi formula, which connects boundary quantum entanglement with bulk geometry, and will tell us more detailed formulation of this connection. We give an interpretation of why such a relationship holds in AdS/CFT based on the tensor network description of bulk geometry. We also generalize both of information theoretic/geometrical objects to multipartite correlation measures, and show that the proposal still works well. arXiv:1708.09393, arXiv:1805.02625

## ODE/DIM meeting

When: 2018/11/26 (Mon.) 13:30-17:00 Honkan (Main Bldg.) H2-39 Katsushi Ito^a , Koichi Harada^b (^a Tokyo Tech, ^b Univ. Tokyo) 13:30-15:00 speaker: Katsushi Ito　(TokyoTech) title: TBA and QM 15:30-17:00 speaker: Koichi Harada (Univ. Tokyo) title: Plane Partition Realization of (Web of) W-algebra Minimal Models

## Regular solutions in a deformed Jackiw-Teitelboim model

When: 2018/11/21 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Suguru Okumura (Kyoto University) We study deformations of a particular (1+1)-dimensional dilaton gravity model, so called the Jackiw-Teitelboim (JT) model, by employing the Yang-Baxter deformation technique. In a original frame, the deformation makes the spacetime structure around the boundary change drastically and a new naked singularity appears. However, by employing a Weyl transformation to the deformed model, we obtain a Liouville dilaton gravity model with a cosmological constant term. Then regular solutions can be constructed by using SL(2) transformations. For a black hole solution, the Bekenstein-Hawking entropy is computed from the area law. This entropy can also be reproduced by evaluating the boundary stress tensor with an appropriate counter-term. arXiv:1801.10537

## Instanton effects in the Hofstadter model

When: 2018/11/14 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Yasuyuki Hatsuda (Rikkyo Univ.) I will review a geometric approach to quantum mechanical spectral problems. As a result, we can systematically compute instanton corrections to the spectrum by using string theory. I first explain it for a very simple model, well-known as the Mathieu equation, and then apply it to more realistic model, the Hofstadter model, which is a two-dimensional electron system in a uniform magnetic field. arXiv:1806.11092

## Resurgence analysis of 2d Yang-Mills theory on a torus

When: 2018/11/07 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Kazuhiro Sakai (Meiji Gakuin Univ.) We study the large $N$ 't Hooft expansion of the partition function of 2d $U(N)$ Yang-Mills theory on a torus. We compute the $1/N$ genus expansion of both the chiral and the full partition function of 2d Yang-Mills using the recursion relation found by Kaneko and Zagier with a slight modification. Then we study the large order behavior of this genus expansion, from which we extract the non-perturbative correction using the resurgence relation. It turns out that the genus expansion is not Borel summable and the coefficient of 1-instanton correction, the so-called Stokes parameter, is pure imaginary. We find that the non-perturbative correction obtained from the resurgence is reproduced from a certain analytic continuation of the grand partition function of a system of non-relativistic fermions on a circle. Our analytic continuation is different from that considered in hep-th/0504221. arXiv:1806.00189

## ゲージ・重力対応における非平衡相転移の臨界指数の解析

When: 2018/10/31 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 中村　真 (中央大学) 非平衡系の物理学は現代物理学における重要なテーマの一つであるが、同時に非平衡統計物理学の構成は難問の一つであることも知られている。非平衡系の扱いが難しい理由は、ミクロな理論から出発してマクロな物理量を得る上で、詳細つり合いの原理や等重率の原理など、平衡系で用いることのできた基本原理を使用できないことにある。一方でゲージ・重力対応においてゲージ相互作用をする粒子の多体系を重力理論にマップすると、重力理論側には自然にブラックホール時空が現れ、温度などのマクロな概念が現れる。すなわち、ミクロとマクロをつなぐ「からくり」が重力理論には存在している。系の境界条件を適切に設定することで外力で駆動される非平衡系を設定することもできることから、このゲージ・重力対応を、散逸の存在する非平衡状態の解析に応用する研究も近年さかんになされている。本研究では、ゲージ・重力対応を用いて、外部電場に沿って定常電流が流れる非平衡定常状態を、線形応答を超えた領域において解析する。文献[1]では、この非線形領域において電気伝導度が転移する、電流駆動型の非平衡相転移が発見され、2次相転移点におけるβおよびδに対応する臨界指数が計算された。本研究[2]では、新たに電流に対する感受率を定義し、その振る舞いからγに対応する臨界指数を計算した。得られた結果はいずれも平衡系のランダウ理論で予想される臨界指数の値と一致する。このことから、ここで扱う非平衡相転移の背後には、ランダウ理論に類似の何らかの有効理論が存在することが示唆される。一方で、単純にはランダウ理論を構成しにくい事情も存在する。本講演では解析の詳細と関連する考察について解説する。 [1] S.N. Nonequilibrium Phase Transitions and Nonequilibrium Critical Point from AdS/CFT,'' Phys. Rev. Lett. 109 (2012) 120602. [2] M. Matsumoto and S.N. Critical Exponents of Nonequilibrium Phase Transitions in AdS/CFT Correspondence,'' arXiv:1804.10124 [hep-th].

## Escaping the branched polymer phase in dynamical triangulations

When: 2018/07/25 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Luca Jose Lionni (YITP, Kyoto University) I will give an overview of some recent developments concerning the combinatorics of triangulations in arbitrary dimension, and explain why they are deeply involved in discrete quantum gravity (dynamical triangulations) and in the study of random tensor models.