# 次回のセミナー (Next Seminar)

## TBA

When: 2017/11/22 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Kazumi Okuyama (Shinshu Univ.) TBA

# 最近のセミナー (Recent Seminars)

## Part1: Chiral algebras and Schur index of N=2 SCFTs / Part2: N=2 S-duality revisited

When: 2017/11/24 (Fri.) 13:30-16:30 Honkan (Main Bldg.) H2-39 Takahiro Nishinaka (Ritsumeikan Univ.) In the first part of this talk, I will review two-dimensional chiral algebras associated with 4d N=2 superconformal field theories (SCFTs). The associated chiral algebra is especially useful for studying strongly coupled SCFTs. I will particularly review the list of 4d superconformal multiplets that contain BPS local operators mapping to 2d chiral algebra operators. In the second part, I will talk about our own work on the chiral algebra of an exotic Argyres-Douglas (AD) theory. This AD theory arises in the strong coupling limit of an exactly marginal SU(3) gauging of simpler AD theories (plus fundamental hypermultiplets), and therefore is an AD version of the Minahan-Nemeschansky E_6 theory arising in the strong coupling limit of the SU(3) gauge theory with six flavors. We argue that this exotic AD theory splits into a free hypermultiplet and a smaller exotic AD theory. We then construct the associated chiral algebra for the latter AD theory, which turns out to be an exotic W-algebra that exists only for special values of the Virasoro central charge. C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli, B.C. van Rees, arXiv:1312.5344 [hep-th], M. Buican, Z. Laczko, T. Nishinaka, arXiv:1706.03797 [hep-th]

## The supersymmetric affine Yangian

When: 2017/11/24 (Fri.) 10:30-12:00 Honkan (Main Bldg.) H155B Hong Zhang (ITP, Beijing) TBA

## TBA

When: 2017/11/22 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Kazumi Okuyama (Shinshu Univ.) TBA

## ABJM理論の非摂動効果とその周辺

When: 2017/11/20 (Mon.) 10:45-16:35 Honkan (Main Bldg.)H113 Kazumi Okuyama (Shinshu Univ.) [日程] 11月20 (月) 10:45-12:15 13:20-14:50 15:05-16:35 11月21 (火) 10:45-12:15 13:20-14:50 15:05-16:35 11月22 (水) 10:45-12:15 13:20-14:50 [講義の目的] M2ブレーンの低エネルギー有効作用であるABJM理論は、AdS/CFT対応によりAdS(4)xS(7)上のM理論に対応している。ABJM理論の球面上の分配関数の解析から、M理論の非摂動効果の理解に最近大きな進展があった。この講義では、ABJM理論の非摂動効果について概観する。 [講義計画] 1. 非摂動効果の概観 2. ABJM模型のplanar極限 3. フェルミガス表示 4. 量子周期とNekrasov-Shatashvili極限 5. 厳密な大分配関数の例 6. 関連する話題 [教科書・参考書等] 特になし

## Reflection States in Ding-Iohara-Miki Algebra and Brane-Web for D-type Quiver

When: 2017/11/08 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Masayuki Fukuda (Tokyo Univ. ) Instanton partition functions of N=1 5d Super Yang-Mills reduced on S1 can be engineered in type IIB string theory from the (p,q)-branes web diagram. To this diagram is superimposed a web of representations of the Ding-Iohara-Miki (DIM) algebra that acts on the partition function. In this correspondence, each segment is associated to a representation, and the (topological string) vertex is identified with the intertwiner operator constructed by Awata, Feigin and Shiraishi. We define a new intertwiner acting on the representation spaces of levels (1,n)⊗(0,m)→(1,n+m), thereby generalizing to higher rank m the original construction. It allows us to use a folded version of the usual (p,q)-web diagram, bringing great simplifications to actual computations. Moreover, reflection states are introduced in the vertical and horizontal modules of the DIM. Extending the correspondence to the vertical reflection states, it is possible to engineer the N=1 quiver gauge theory of D-type (with unitary gauge groups). In this way, the Nekrasov instanton partition function is reproduced from the evaluation of expectation values of intertwiners. This computation leads to the identification of the vertical reflection state with the orientifold plane of string theory.

## A 2D dilaton gravity model with hyperbolic potential

When: 2017/11/01 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Hideki Kyono (Kyoto Univ.) Recently, 2D dilaton gravity is drawing attention as a toy model of holography. We consider a system with a hyperbolic dilaton potential associated with an integrable deformation of the Almheiri-Polchinski model. Even in the deformed case, the system has the general solution. Especially, it has a black hole solution and we reproduce its Bekenstein-Hawking entropy from the viewpoint of the boundary stress tensor by taking an appropriate counterterm. Finally, we will discuss some solutions with matter fields. This seminar talk is based on our recent works (arXiv: 1701.06340 and 1704.07410) with S.Okumura and K. Yoshida. arXiv:1701.06340, arXiv:1704.07410

## Fermion scattering amplitudes from gauge-invariant actions for open superstring field theory

When: 2017/10/13 (Fri.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Hiroki Sukeno (Univ. Tokyo, Komaba) Superstring field theory is a formulation of superstring theory based on the spacetime gauge invariance. On the other hand, an essential ingredient that ensures decoupling of unphysical degrees of freedom in the world-sheet theory is the integration over the supermoduli space of super-Riemann surfaces. It is important to understand how this integration over the supermoduli space is implemented in superstring field theory based on spacetime gauge invariance. In this talk, we calculate on-shell scattering amplitudes involving fermions at the tree level in open superstring field theory. In particular, we calculate four-point and five-point amplitudes from open superstring field theory constructed by Kunitomo and Okawa, and we elucidate how the amplitudes in the world-sheet path integral with the standard prescription using picture-changing operators are reproduced. arXiv:1612.00777

## Supermatrix Chern-Simons Model

When: 2017/09/20 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Tadashi Okazaki (National Taiwan University) We will discuss matrix Chern-Simons quantum mechanics. The model is known to be equivalent to the Calogero model and is proposed as an effective theory of quantum Hall states and of vortices in Chern-Simons theory. Recently Dorey, Tong and Turner generalized the model (arXiv:1603.09688, arXiv:1604.05711) and demonstrate that it can capture more general quantum Hall states with spin degrees of freedom of underlying electrons. Also in the large N limit, it turns out to be closely related to the WZW model. We will review several aspects of the model involving recent results and discuss ongoing work which is a further generalization of this matrix model whose symmetry group is extended to a supergroup.

## $\mathcal{N}=1$ Deformations and RG Flows of $\mathcal{N}=2$ SCFTs

When: 2017/07/26 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Kazunobu Maruyoshi (Seikei Univ.) We study certain $\mathcal{N}=1$ preserving deformations of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) with non-Abelian flavor symmetry. The deformation is described by adding an $\mathcal{N}=1$ chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving the nilpotent vacuum expectation value to the chiral multiplet. Remarkably, we find classes of theories flow to $\mathcal{N}=2$ supersymmetric fixed points in the infrared under the deformation. In particular, we find renormalization group flows from the deformed conformal SQCDs with gauge group $SU(N)$ and $Sp(N)$ to $\mathcal{N}=2$ SCFTs of Argyres-Douglas type. From these "Lagrangian descriptions," we compute the full superconformal indices and find agreements with the previous results. This talk is based on the collaboration with Prarit Agarwal and Jaewon Song, and arXiv:1606.05632, arXiv:1607.04281, arXiv:1610.05311. arXiv:1606.05632, arXiv:1607.04281, arXiv:1610.05311.

## Refined large N duality for knots

When: 2017/07/12 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Masaya Kameyama (Nagoya Univ.) I will talk about large N duality of refined Chern-Simons theory with a knot. Chern-Simons theory provides a natural framework of quantum invariants of three-manifolds and knots and it is known that its large N limit is dual to topological string theory on the resolved conifold. Motivated by knot homology, refinements of Chern-Simons theory, BPS states and topological string have been studied since Gukov-Schwarz-Vafa’s work. Our formulation gives a relation between refined Chern-Simons invariants of a knot and refined BPS states in the resolved conifold, which is a generalization of the work of Labastida-Mrino-Ooguri-Vafa in refined topological string theory, and extends the proposal of Gukov-Schwarz-Vafa to any colors. arXiv:1703.05408

## 2017 年度 第 1 回日露ワーキングセミナー

When: 2017/07/08 (Sat.) 10:30-15:30 Honkan (Main Bldg.) H2-39 今野 均$^a$, 初田泰之$^b$ ($^a$東京海洋大学, $^b$立教大学) Talk1: 10:30~12:30 Speaker: 今野 均（東京海洋大学） Title: 楕円量子群 U_{q,p}(\widehat{\mathfrak{g}}) の表現と応用:楕円q-KZ方程式, 楕円重み関数, Gelfand-Tsetlin基底上の有限次元表現 Abstract: 最初に, 楕円可解格子模型などとの関連から楕円量子群 U_{q,p}(\widehat{\mathfrak{g}})を 定式化した経緯や, ３通りの定式化, quasi-Hopf algebra {\cal B}_{q,\lambda}(\widehat{\mathfrak{g}}), FRST流(Felderの楕円量子群), Drinfeld流 U_{q,p}(\widehat{\mathfrak{g}}), 相互の関連について簡単に話をする. 続いて, 最近得た結果に基づいて U_{q,p}(\widehat{\mathfrak{ sl}}_N) の表現を用いた楕円 q-KZ方程式の形式的積分解の導出, 特にその被積分関数に現れる楕円重み関数の導出とその性質, 及びそれらと U_{q,p}(\widehat{\mathfrak{ gl}}_N) のGelfand-Tsetlin基底上の 有限次元表現との関連について述べる. この表現は Vasserotや中島による量子アフィン代数U_q(\widehat{\mathfrak{g}}) の同変K理論上の幾何学的表現の自然な楕円関数型拡張になっている. 楕円重み関数は, Aganagic-Okounkovによって同変楕円コホモロジーに付随して定式化された楕円stable envelopに同一視され, また, その対応に基づいて, Gelfand-Tsetlin基底上の有限次元表現は同変楕円コホモロジー上の幾何学的表現を与えることが期待される.　時間があれば, 量子 q -Langlands双対性についても触れる. Talk2: 13:30~15:30 Speaker: 初田泰之（立教大学） Title: Calabi-Yau geometry and electrons on 2d lattices Abstract: I will talk about our recent results on a novel relation between toric Calabi-Yau geometry and certain electron systems on 2d lattices. It turns out that the modular double duality, known in quantum group, plays an important role.

## Supersymmetric Renyi Entropy and Defect Operators

When: 2017/07/05 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Tatsuma Nishioka (Univ. of Tokyo , Hongo) We describe the defect operator interpretation of the supersymmetric Renyi entropies of superconformal field theories in three, four and five dimensions. The operators involved are supersymmetric codimension-two defects in an auxiliary Z_n gauge theory coupled to n copies of the SCFT. We compute the exact expectation values of such operators using localization, and compare the results to the supersymmetric Renyi entropy. The agreement between the two implies a relationship between the partition function on a squashed sphere and the one on a round sphere in the presence of defects. arXiv:1612.02894

## On confinement in Yang-Mills theory

When: 2017/06/28 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Kazuya Yonekura (Kavli IPMU) I will discuss some aspects of confinement in Yang-Mills theory in a weak coupling setup. The theory is put on a three-dimensional torus, and the relation between four dimensional Yang-Mills theory and two dimensional CPN model is discussed and used to derive properties of Yang-Mills theory in the confining phase. Then the vacuum structure of Yang-Mills theory which are usually associated to strong coupling dynamics will be discussed in completely weakly coupled regime. arXiv:1704.05852, arXiv:1706.06104

## Refined geometric transition and qq-characters

When: 2017/06/21 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Yuji Sugimoto (Osaka Univ.) We provide the refined prescription for the geometric transition in the refined topological string theory and show how to apply it to constructing doubly quantized Seiberg-Witten curves called qq-characters. In the arguments of literatures for the refined geometric transition, it was not seriously considered that the choice of the preferred direction may affect the open string amplitude. Our prescription given here for the refined geometric transition is involved in nontrivial effects from sensitivity to the preferred direction. As its application, we discuss the description of the qq-character that was recently well-developed but whose stringy origin is still unclear. It is proposed that it can be engineered by the refined geometric transition, which may possibly give interpretation in terms of string theory. arXiv:1705.03467

## Calabi-Yau geometry and electrons on 2d lattices

When: 2017/06/16 (Fri.) 13:30-14:30 Honkan (Main Bldg.) H2-39 Yasuyuki Hatsuda (Rikkyo Univ.) I will talk about our recent results on a novel relation between toric Calabi-Yau geometry and certain electron systems on 2d lattices. It turns out that the modular double duality, known in quantum group, plays an important role. arXiv:1701.01561

## On the transverse M5-branes in matrix theory

When: 2017/05/31 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Shinji Shimasaki (Keio University) It has been a long-standing problem how the transverse M5-branes are described in the matrix-model formulations of M-theory. We consider this problem for M-theory on the maximally supersymmetric pp-wave geometry, which admits transverse spherical M5-branes with zero light-cone energy. By using the localization, we directly analyze the strong coupling region of the corresponding matrix theory called the plane wave matrix model (PWMM). Under the assumption that the low energy modes of the scalar fields in PWMM become mutually commuting in the strong coupling region, we show that the eigenvalue density of the SO(6) scalars in the low energy region exactly agrees with the shape of the spherical M5-branes in the decoupling limit. This result gives a strong evidence that the transverse M5-branes are indeed contained in the matrix theory and the theory realizes a second quantization of the M-theory. arXiv:1701.07140

## AdS from Optimization of Path-Integrals in CFTs

When: 2017/05/24 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Kento Watanabe (YITP) 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. arXiv:1703.00456

## Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders in the CP1 quantum mechanics

When: 2017/05/12 (Fri.) 13:30-14:30 Honkan (Main Bldg.) H2-39 Toshiaki Fujimori (Keio University) Perturbation series in quantum theory are usually divergent asymptotic series which give rise to ambiguities when they are resummed by using the Borel resummation. Those ambiguities are expected to be canceled when non-perturbative corrections from non-trivial saddle points are correctly added to form so-called resurgent trans-series. In this seminar, I will talk about the full resurgent trans-series in the (nearly) supersymmetric ℂP1 quantum mechanics reduced from the 2d N=(2,0) model. We obtain exact results for the first and second susceptibility of the ground state energy under a SUSY breaking deformation. They are absolutely convergent series of nonperturbative exponentials corresponding to multi-bions saddle points. We obtain all multi-bion exact solutions in the complexified theory and construct the resurgent trans-series to all orders in the multi-bion contributions. We show that it reproduces the exact result, which supports the resurgence to all orders. arXiv:1702.00589

## Boundary conditions of topological materials and edge-of-edge state

When: 2017/04/26 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Taro Kimura (Keio University) The existence of gapless edge states localized on the boundary is one of the most important aspects of the topological materials. We consider how to systematically characterize the boundary condition of such a topological system, and study how the edge state depends on that. Typically co-dimension of the boundary is just one, but we can consider a higher co-dimension boundary, and the gapless state localized on it, which we call edge-of-edge state, by applying several boundary conditions simultaneously. We show that such an edge-of-edge state actually can exist with a toy model, which is a Weyl semimetal, and also discuss its experimental realization. This talk is based on a collaboration with K. Hashimoto and X. Wu (Osaka U): [arXiv:1609.00884] [arXiv:1702.00624]. arXiv:1609.00884, arXiv:1702.00624

## Recent developments in Effective String Theory

When: 2017/04/12 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Shunsuke Maeda (Univ. of Tokyo, IPMU) In this talk I will review the universal effective two-dimensional field theory which describes the dynamics of relativistic confining flux tubes in an arbitrary number of spacetime dimensions. I will then discuss more recent developments including the construction of vertex operators which represent off-shell background fields. Finally, as an simple application I will show how to compute a scalar form factor of a long string from these vertex operators. arXiv:1701.06406

## Correlation functions in N=4 SYM from hexagons

When: 2017/03/24 (Fri.) 13:30-15:30 Honkan (Main Bldg.) H2-39 Shota Komatsu (Perimeter Institute) I will overview the recent development to compute correlation functions in planar N=4 SYM using integrability. The key player in the story is a "square-root" of three-point function, which we call hexagon. I will first show that the three-point function can be decomposed into two hexagons and, by gluing them back together, one can (in principle) compute the structure constants non-perturbatively. I will then explain that a similar idea can work also for four-point functions by showing it explicitly at one loop. The method provides an alternative way to decompose the higher-point function, which is different from the usual OPE expansion.