# 次回のセミナー (Next Seminar)

## Commutative Geometry for Non-commutative D-branes by Tachyon Condensation

When: 2018/07/04 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 So Matsuura (Keio University) The position of D-brane system is usually determined by the U(1) part of the scalar fields on it. However, when the scalar fields on D-branes are mutually non-commutative, this interpretation does not work always and the position of the non-commutative D-branes in the commutative space-time becomes far from trivial. In this talk, I will propose a way to determine the position or the shape of such non-commutative D-brane systems from the view point of the tachyon condensation. In particular, I will discuss the relation to the so called coherent state method developed in the context of matrix geometry. arXiv:1804.00161

# 最近のセミナー (Recent Seminars)

## TBA

When: 2018/07/25 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Luca Jose Lionni (YITP, Kyoto University) TBA

## TBA

When: 2018/07/18 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Kenta Shiozawa (Kitasato Univ.) TBA arXiv:1803.11087

## TBA

When: 2018/07/11 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Toshiaki Fujimori (Keio Univ.) TBA

## Commutative Geometry for Non-commutative D-branes by Tachyon Condensation

When: 2018/07/04 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 So Matsuura (Keio University) The position of D-brane system is usually determined by the U(1) part of the scalar fields on it. However, when the scalar fields on D-branes are mutually non-commutative, this interpretation does not work always and the position of the non-commutative D-branes in the commutative space-time becomes far from trivial. In this talk, I will propose a way to determine the position or the shape of such non-commutative D-brane systems from the view point of the tachyon condensation. In particular, I will discuss the relation to the so called coherent state method developed in the context of matrix geometry. arXiv:1804.00161

## Construction of K3 surfaces that uses the quadratic base change and U(1) gauge symmetries in F-theory compactifications

When: 2018/06/06 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Yusuke Kimura (KEK) We discuss F-theory compactifications with U(1) gauge symmetries of various ranks. We consider compactifications on the direct products of K3 surface, in which one of K3 surfaces in a product is elliptically fibered. We construct elliptic K3 surfaces with various Mordell-Weil ranks to build F-theory models with U(1) symmetries. Because the sum of the ranks of the singularity type and the Mordell- Weil group of a rational elliptic surface is always 8, families of rational elliptic surfaces with a section with various Mordell-Weil ranks can be constructed by fixing the singularity types. Gluing pairs of identical rational elliptic surfaces yields elliptic K3 surfaces. The Mordell-Weil group of an original rational elliptic surface is a subgroup of the Mordell-Weil group of the resulting K3 surface. Therefore, the Mordell-Weil rank of the resulting K3 surface is equal to, or greater than the Mordell-Weil rank of the original rational elliptic surface. Using this fact and by gluing pairs of identical rational elliptic surfaces, we construct families of K3 surfaces, F-theory compactifications on which have U(1) gauge symmetries of various ranks. We determine the Weierstrass equations of these K3 surfaces. We also discuss non-Abelian gauge symmetries that arise in F-theory compactifications. JHEP 05(2018)048 (arXiv:1802.05195), JHEP 03(2018)045 (arXiv:1710.04984)

## Exploring the quantum gravity via the observer dependence in black holes

When: 2018/06/01 (Fri.) 13:30-14:30 Honkan (Main Bldg.) H2-39 Kanato Goto (Tokyo univ.) One of the pronounced characteristics of gravity, distinct from other interactions, is that there are no local observables which are independent of the choice of the spacetime coordinates. This property acquires crucial importance in the quantum domain in that the structure of the Hilbert space pertinent to different observers can be drastically different. Such intriguing phenomena as the Hawking radiation and the Unruh effect are all rooted in this feature. As in these examples, the quantum effect due to such observer-dependence is most conspicuous in the presence of an event horizon and there are still many questions to be clarified in such a situation. In this talk, we attempt to perform a comprehensive study of the observer dependence of the quantum Hilbert space of a massless scalar field in the vicinity of the horizon of the Schwarzschild black holes in four dimensions, both in the eternal (two-sided) case and in the physical (one-sided) case created by collapsing matter. Specifically, we compare and relate the Hilbert spaces of the three types of observers, namely (i) the freely falling observer, (ii) the observer who stays at a fixed proper distance outside of the horizon and (iii) the natural observer inside of the horizon analytically continued from outside. The relations we obtain have a number of important implications, such as on the quantum equivalence principle and the related firewall phenomenon, on the number of degrees of freedom seen by each type of observer, and on the “thermal-type” spectrum of particles realized in a pure state. arXiv:1803.01672

## Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT

When: 2018/05/23 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Masamichi Miyaji (YITP) In this talk, I will discuss how AdS space emerges from tensor network. First I explain the way to formulate continuous tensor networks for general interacting QFTs, using Euclidean path integral and Weyl transformation. Then I describe our new proposal which identifies this Weyl factor as metric in the bulk. Finally, I explain how to fix this Weyl factor by "optimization of path integral", and show that correct geometries, predicted by AdS/CFT, can be reproduced in several examples. arXiv:1706.07056

## $5$-brane webs and 5d $\mathcal{N}=1$ rank 2 theories

When: 2018/05/09 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Hirotaka Hayashi (Tokai Univ.) We propose $5$-brane web diagrams for 5d $\mathcal{N}=1$ $G_2$ gauge theories. Intriguingly, the $G_2$ gauge group is realized from a 5-brane web with an $\text{O5}-$plane or an $\widetilde{\text{O5}}-$plane. Based on the obtained 5-brane webs, we compute the partition functions for the 5d $G_2$ gauge theories using the topological vertex formalism with an $\text{O5}-$plane, and we find agreement with known results. Furthermore, it is also possible to see recently proposed dualities among $G_2$, $\text{SU}(3)$ and $\text{Sp}(2)$ gauge theories from the 5-brane web diagrams. arXiv:1801.03916

## Borel summability of supersymmetric ’t Hooft loop -effect of monopole bubbling-

When: 2018/04/25 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Daisuke Yokoyama (Fudan Univ.) I will explain our recent result [arXiv:1711.10799 ], which discuss Borel summability of ’t Hooft loop in 4d N=2 supersymmetric gauge theories. Borel summability is highly related to non-perturbative effects (instanton effects, bubbling effect etc.), which can be seen in a context of resurgence. I will start with preliminaries like definitions of Borel resummation, minimal explanation on resurgence, instanton, ’t Hooft loop and monopole bubbling effect in our context. Finally, we will discuss our result showing that the ’t Hooft loop is Borel summable. arXiv:1711.10799

When: 2018/04/18 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Akinori Tanaka (RIKEN) Recently, machine learning techniques, in particular techniques of deep learning, are unprecedentedly developed.In deep learning, we prepare graphical systems with layered structures called multilayer perceptions (MLPs). MLP includes tunable parameters, and we fix them via some updating algorithm. It is called "training" or "learning" process in machine learning community. In our paper, we suggest an idea of deep learning/AdS correspondence by showing that a system of scalar bosons in AdS background can be mapped to corresponding MLP. In this context, all parameters of the bulk theory including coupling constants and background metric correspond to tunable/learning parameters of the MLP, and we can fix them through learning process by using the boundary data we want to explain. In this talk, I also explain basics of machine learning techniques focusing on MLP and related recent papers. arXiv:1802.08313

## Deformation of N=4 SYM with space-time dependent couplings

When: 2018/02/09 (Fri.) 13:30-14:30 Honkan (Main Bldg.) H2-39 Jose J. Fernandez-Melgarejo (YITP) We will firstly study deformations of N=4 supersymmetric Yang-Mills theory with couplings and masses depending on space-time. The conditions to preserve part of the supersymmetry are derived and a lot of solutions of these conditions are found. The main example is the case with ISO(1,1)×SO(3)×SO(3) symmetry, in which couplings, as well as masses and the theta parameter, can depend on two spatial coordinates. When this case is enhanced to ISO(1,2), we obtain the Janus configuration found by Gaiotto&Witten. Secondly, we will study some of these solutions by embedding probe D3-branes in supergravity backgrounds with non-trivial fluxes. The effective action on the world-volume of the D3-branes is analyzed and a map between the deformation parameters and the fluxes is obtained. Based on [arXiv:1710.09792] and [arXiv:1801.09394] arXiv:1710.09792, arXiv:1801.09394

## Very Special Conformal Field Theories and Holographic duals

When: 2018/01/26 (Fri.) 13:30-14:30 Honkan (Main Bldg.) H2-39 Yu Nakayama (Rikkyo Univ.) Sometime ago Cohen and Glashow introduced the notion of Very Special Relativity, which are subgroups of the Poincare group that preserve one particular null direction. The realization of very special relativity in field theories is a challenging question. Cohen and Gashow even claimed that it is impossible without violating locality. Their argument is based on the spurion analysis, but in this talk, I show there is a loophole in their argument and I present some concrete examples of field theory realization based on the idea of topological twist. I also show new solutions of Einstein equation with matter, motivated from the holographic realization of very special conformal field theories. arXiv:1707.05423.

## Exotic five-branes of codimension two in heterotic supergravity

When: 2018/01/17 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Shin Sasaki (Kitasato Univ.) In this talk, I introduce three (symmetric, neutral, gauge) distinct types of five-branes of codimension two in heterotic supergravity. We study T-duality chains of the five-branes where the famous Buscher rule receives string $\alpha’$-corrections. We explicitly write down the exotic $5^2_2$-brane solutions associated with the symmetric and the neutral types of the NS5-brane. The $O(2,2)$ monodromy structures of the $5^2_2$-brane solutions are investigated by the $\alpha’$-corrected generalized metric. Our analysis shows that the symmetric $5^2_2$-brane solution, which satisfies the standard embedding condition, is a T-fold and it exhibits a non-geometric nature. We also find that the neutral $5^2_2$-brane solution is a T-fold at least at $\mathcal{O}(\alpha’)$. By the Nahm construction of periodic monopoles, we work out the explicit solution of the gauge-type five-brane of codimension two. The $5^2_2$-brane of the gauge-type is shown to be geometric and not a T-fold. arXiv:1608.01436, arXiv:1708.08066.

## Flow equation, conformal symmetry, AdS geometries with general conformally flat boundary

When: 2017/12/22 (Fri.) 13:30-14:30 Honkan (Main Bldg.) H2-39 Shuichi Yokoyama (YITP) In this talk I will speak about my recent works with S.Aoki on the study of mechanism of emergence of AdS geometry from CFT via flow equation. A flow equation is a kind of operator renormalization which resolves UV singularity. While this was used to help numerical simulation in lattice QCD, there has recently been a proposal to construct a one higher dimensional geometry associated with the flow equation in a QFT. In our recent papers, I investigated aspects of an induced metric with the collaborator and our main results are the following. i) Generally an induced metric becomes a quantum information metric called the Bures or Helstrom metric. ii) For any CFT, induced metrics explicitly computed match (Poincare) AdS. iii) Conformal symmetry of CFT converts to the AdS isometry after quantum averaging. This guarantees the emergence of AdS without explicit calculation. iv) We generalize ii) and iii) in the case of any CFT defined on a general conformally flat manifold. arXiv:1707.03982, arXiv:1709.07281

## M2- and M5-branes in E_11 Current Algebra Formulation of M-theory

When: 2017/12/08 (Fri.) 13:30-14:30 Honkan (Main Bldg.) H2-39 Shotaro Shiba (KEK) M-theory may be described in terms of E_11 algebra: All the degrees of freedom, including fields, coordinates and even M-branes, can be elements of E_11 group. Then we propose that equations of motion for M-branes are written down in E_11 algebra, using the current algebra formulation known as Sugawara construction. We also discuss the geometric equations, and show that there are static solutions when M2- or M5-brane exists alone and when M5-brane wraps around M2-brane. The latter situation can be realized because our geometric equation has a deviation from Einstein equation, thus avoiding the usual intersection rule of branes. P. C. West, Phys. Lett. B 575, 333 (2003) [hep-th/0307098]. H. Sugawara, Int. J. Mod. Phys. A 32 (2017) no.05, 1750024 [arXiv:1701.06894 [hep-th]]. S. Shiba and H. Sugawara, arXiv:1709.07169 [hep-th].

## 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) The affine Yangian of gl1 is known to be isomorphic to $W_{1+∞}$, the W- algebra that characterizes the bosonic higher spin – CFT duality. In this paper we propose defining relations of the Yangian that is relevant for the N = 2 superconfor- mal version of $W_{1+∞}$. Our construction is based on the observation that the N = 2 superconformal $W_{1+∞}$ algebra contains two commuting bosonic $W_{1+∞}$ algebras, and that the additional generators transform in bi-minimal representations with respect to these two algebras. The corresponding affine Yangian can therefore be built up from two affine Yangians of gl1 by adding in generators that transform appropriately.

## 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