# 次回のセミナー (Next Seminar)

## M2-branes and 𝔮-Painlevé equations

When: 2022/07/06 (Wed.) 16:00-17:00 Zoom online Naotaka Kubo (Center for Gravitational Physics) We propose that a grand partition function of a 3d gauge theory satisfies a discrete equation which has an integrable structure. The 3d gauge theory is the N=4 superconformal Chern-Simons theory which is a worldvolume theory of M2-branes. The discrete equation is the so-called q-Painleve VI equation, which is a q-analog of the Painleve VI equation. Our proposal comes from a sequence of relations between the 3d gauge theory, quantum curves, a topological string theory, a 5d gauge theory and the q-Painleve equations. In this talk, we first shortly review the gauge theory, the q-Painleve equation and the background explained above. We then explain our proposal and its implications. The implications are not only for the gauge theory but also for the series of the q-Painleve equations. arXiv:2202.10654

# 最近のセミナー (Recent Seminars)

## Brane Dynamics of Holographic BCFTs

When: 2022/07/13 (Wed.) 16:00-17:00 Zoom online Kenta Suzuki (YITP) arXiv:2205.15500

## M2-branes and 𝔮-Painlevé equations

When: 2022/07/06 (Wed.) 16:00-17:00 Zoom online Naotaka Kubo (Center for Gravitational Physics) We propose that a grand partition function of a 3d gauge theory satisfies a discrete equation which has an integrable structure. The 3d gauge theory is the N=4 superconformal Chern-Simons theory which is a worldvolume theory of M2-branes. The discrete equation is the so-called q-Painleve VI equation, which is a q-analog of the Painleve VI equation. Our proposal comes from a sequence of relations between the 3d gauge theory, quantum curves, a topological string theory, a 5d gauge theory and the q-Painleve equations. In this talk, we first shortly review the gauge theory, the q-Painleve equation and the background explained above. We then explain our proposal and its implications. The implications are not only for the gauge theory but also for the series of the q-Painleve equations. arXiv:2202.10654

## Kazakov-Migdal Model and Graph Zeta Functions

When: 2022/06/29 (Wed.) 16:00-17:00 Honkan (Main Bldg.) H2-39 Kazutoshi Ohta (Meiji Gakuin Univ.) We show that a generalized Kazakov-Migdal model defined on the graph can be represented by the unitary matrix integral of the weighted graph zeta functions, which have series expansions by possible Wilson loops (graph cycles). The partition function of the model is expressed in two different ways according to the order of integration. When the parameters of this model are appropriately tuned, a specific unitary matrix integral can be performed at any finite N thanks to this duality. We exactly evaluate the partition function of the parameter-tuned Kazakov-Migdal model on an arbitrary graph in the large N limit and show that it is expressed by the infinite product of the Ihara zeta functions of the graph. We also discuss other generalizations and applications of the graph zeta functions. arXiv:2204.06424

## Global anomalies in 8d supergravity

When: 2022/06/22 (Wed.) 16:00-17:00 Zoom online Kazuya Yonekura (Tohoku univ.) I discuss global anomalies in eight dimension, focusing on 8d supergravity. Fermions like gaugino and gravitino turn out to have anomalies.Then I discuss how they can be cancelled by other fields. One mechanism is a nonperturbative version of the Green-Schwarz mechanism. Another mechanism is by topological degrees of freedom. The anomaly cancellation mechanisms impose constraints on the topology of spacetime. arXiv:2203.12631

## M2-branes and plane partitions

When: 2022/06/01 (Wed.) 16:00-17:00 Zoom online Tadashi Okazaki (KIAS) There is a correspondence between the protected local operators in the 3d SCFTs describing the geometry C^2 probed by a stack of N M2-branes and plane partitions of trace N. We discuss combinatorial expressions of the indices which count the local operators parametrizing C^2/Z_k probed by N M2-branes in the canonical and grand canonical ensembles in terms of generating functions for plane partitions. If time permits, we also discuss further applications and questions including the asymptotic behaviors of the grand potential in the high-temperature limit and the scaling dimension in the large N limit. arXiv:2204.01973
When: 2022/05/27 (Fri.) 13:30-14:30 Zoom Kazushi Yamashiro (Shizuoka) arXiv:2201.06871

## String theory, N=4 SYM and Riemann hypothesis

When: 2022/05/18 (Wed.) 16:00-17:00 Zoom online Masazumi Honda (YITP) We discuss new relations among string theory, four-dimensional N=4 supersymmetric Yang-Mills theory (SYM) and the Riemann hypothesis. It is known that the Riemann hypothesis is equivalent to an inequality for the sum of divisors function σ(n). Based on previous results in literature, we focus on the fact that σ(n) appears in a problem of counting supersymmetric states in the N=4 SYM with SU(3) gauge group: the Schur limit of the superconformal index plays a role of a generating function of σ(n). Then assuming the Riemann hypothesis gives bounds on information on the 1/8-BPS states in the N=4 SYM. The AdS/CFT correspondence further connects the Riemann hypothesis to the type IIB superstring theory on AdS5×S5. In particular, the Riemann hypothesis implies a miraculous cancellation among Kaluza-Klein modes of the supergravity multiplet and D3-branes wrapping supersymmetric cycles in the string theory. We also discuss possibilities to gain new insights on the Riemann hypothesis from the physics side. This talk is based on a collaboration with Takuya Yoda (arXiv:220317091). arXiv:2203.17091

## The colored Jones polynomials as vortex partition functions

When: 2022/04/22 (Fri.) 13:30-14:30 Zoom Masahide Manabe (大阪公立大学) The colored Jones polynomials, which are obtained as the Wilson loop expectation values along knots in $SU(2)$ Chern-Simons gauge theories, detect the same knots and strongly distinguish inequivalent knots. In this talk, I will present a construction of $3$D$\mathcal{N}=2$ abelian gauge theories on $\mathbb{S}^2 \times \mathbb{S}^1$ whose vortex vortex partition functions yield the colored Jones polynomials of knots in $\mathbb{S}^3$. This is based on arXiv:2110.05662, a joint work with Seiji Terashima and Yuji Terashima. arXiv:2110.05662

## $\rm{dS}_3/\rm{CFT}_2$ correspondence

When: 2022/04/13 (Wed.) 16:00-17:00 Zoom Yasuaki Hikida (YITP) In order to understand quantum gravity on a cosmological background, dS/CFT correspondence is expected to be useful as in the case of AdS/CFT correspondence. However, dS/CFT correspondence has not been well understood yet, and as a reason only a few concrete examples are available currently. In this talk, I will explain our recent proposal on dS/CFT correspondence between 3d classical Einstein gravity and 2d SU(2) WZW model at the critical level. For supporting arguments, we examine partition functions, correlation functions, and relation to higher-spin $\rm{AdS}_3$ holography. arXiv:2203.02852

## Understanding DAHA from physics

When: 2022/02/02 (Wed.) 11:00-14:00 Zoom Satoshi Nawata (Fudan University) Double affine Hecke algebra (DAHA) was introduced by Cherednik around the mid-90s. In the first half of the talk, I will explain DAHA of A_1 type and its representation from 2d sigma-model on Hitchin moduli space of once-punctured torus. This approach gives a geometric viewpoint of DAHA representations. In the second half, I will connect the 2d sigma model to 3d modularity and an algebra of line operator of a 4d N=2^* theory. The dimensional uplift provides a categorical perspective of DAHA and its representations. Part I 11:00-12:00 Part II13:00-14:00

## Supersymmetric vortex loops in 3D gauge theories

When: 2022/01/26 (Wed.) 11:00-12:00 Zoom online Kazuo Hosomichi (National Defense Academy of Japan) We give a precise definition of BPS vortex loops in 3D non-abelian gauge theories with N=2 SUSY by the path integral over fields with a prescribed singular behavior. We compute the expectation value of a BPS vortex loop on an ellipsoid. Using the result we revisit the known equivalence between Wilson and vortex loops in pure Chern-Simons theory. Naive computations of expectation values in N=2 theory leads to an unwanted shift of parameters in the rule of correspondence. We resolve the problem by relating the shift to the global anomaly of N=2 SUSY quantum mechanics. For theories with U(N) gauge group we also develop an alternative description of vortex loops in terms of 1D N=2 SUSY quantum mechanics on their worldline. For vortex loops in N=4 theories, our construction reproduces some of the quiver GLSMs of Assel and Gomis. arXiv:2111.04249

## Entanglement entropy and two-point functions of operators

When: 2022/01/19 (Wed.) 11:00-12:00 Zoom online Katsuta Sakai (KEK) Entanglement entropy (EE) is one of the basic measure for the quantum entanglement between subsystems. In order to connect such an entanglement with realistic observables, it is inevitable to study EE in general interacting field theory. In this talk, I will present our analysis in the case where the subsystem is a half-space, and give a formula for would-be-dominant contribution to EE in terms of two-point functions of various operators, in which quantum corrections are taken into account. Then, in attempt to generalize the result and to grasp the underlying structure, I will reconsider EE for a general subsystem in the free theory case, which is expressed with two-point function of the fundamental fields. I also discuss the interacting case as an ongoing analysis. arXiv:2105.02598

## Non-invertible topological defects in 4-dimensional $Z_2$ pure lattice gauge theory

When: 2021/12/15 (Wed.) 11:00-12:00 Honkan (Main Bldg.) H2-39 Masataka Koide (Osaka Univ.) In recent years, the extension of the notion of symmetry using the picture of topological defects and their applications have been actively studied. One direction is the so-called “non-invertible symmetry”, in which non-invertible topological defects are treated as “symmetry”. Non-invertible symmetries in two dimensions have been actively investigated, but on the other hand, in higher dimensions are relatively less understood. In this talk, we explore topological defects in the 4-dimensional pure $Z_2$ lattice gauge theory. This theory has 1-form $Z_2$ center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We have constructed non-invertible topological defects from the KWW duality and $Z_2$ center symmetry defect in a similar way to those constructed by the Aasen, Mong, Fendley for the 2-dimensional Ising model. We also constructed the junction that occurs where the two defects overlap. The KWW duality defect is non-invertible, so it is not necessary to be invariant under deformations that change the topology. For such deformations, the topological relation can be made closed by including $Z_2$-center symmetry defects and junctions. This equation can be used to calculate the expectation values of some configurations of the KWW duality defect. arXiv:2109.05992

## Integrable sigma models from 4d Chern-Simons theory

When: 2021/12/08 (Wed.) 11:00-12:00 Zoom Osamu Fukushima (Kyoto University) The 4d Chern-Simons (CS) theories are a unifying framework of $2$d integrable field theories and lattice models. Constructions of integrable field theories from $4$d CS theories are based on two classes: order and disorder defects. Based on each of these aspects, I will talk about systematic derivations of integrable sigma models. In particular, I will explain how coset structures are presented in $4$d CS theories. The derivations include supercoset sigma model and its integrable deformation for disorder defects, and non-abelian Toda field theories for order defects. arXiv:2005.04950

## Chaotic string dynamics in deformed T^{1,1}

When: 2021/12/01 (Wed.) 11:00-12:00 Zoom online Takaaki Ishii (Rikkyo University) Testing (non-)integrability is significant for identifying geometries of interest. Recently, Arutyunov, Bassi and Lacroix have shown classical integrability of the string sigma model with a deformed T^{1,1} background equipped with a Kalb-Ramond two-form at a critical value (arXiv:2010.05573 [hep-th]). Meanwhile, the sigma model was also conjectured to be non-integrable when the two-form is off critical. I will talk about confirming this conjecture by explicitly presenting classical chaos in the dynamics of a winding string. This talk is based on arXiv:2103.12416 [hep-th] arXiv:2103.12416

## Quiver Quantum Toroidal Algebra and Crystal Representations

When: 2021/11/10 (Wed.) 11:00-12:00 Zoom online Akimi Watanabe (Tokyo Univ.) This talk is based on arxiv:2101.03953, 2108.07104, and 2109.02045. We proposed a new class of algebras, Quiver Quantum Toroidal Algebra, a generalization of Quantum Toroidal $gl_1$. It is known that Quantum Toroidal $gl_1$ has representations by 1d, 2d, and 3d Young diagrams. (Shifted) Quiver Quantum Toroidal Algebra acts on more general 1d, 2d, and 3d crystals. We study the way of constructing 2d crystals representations from 1d crystals representations. arXiv:2101.03953, arXiv:2108.07104, arXiv:2109.02045

## Anomaly-induced edge currents in hydrodynamics with parity anomaly

When: 2021/10/29 (Fri.) 12:30-13:30 Zoom online Takuya Furusawa (Tokyo Institute of Technology) In this talk, we investigate hydrodynamic transports of the massless Dirac fermion in (2+1) dimensions. This system often appears in planar topological matters and on the boundary of topological insulators. Besides, it has a global ’t Hooft anomaly between U(1) and parity symmetries called the parity anomaly. We study how the relativistic hydrodynamics implements the parity anomaly, particularly focusing on the transport phenomena at the boundary. In the absence of the boundary, the parity anomaly matching yields only a bulk anomalous current with vanishing divergence [1,2]. On the other hand, combining the consideration of the boundary and the second law of local thermodynamics, we find that the parity anomaly also causes U(1) and entropy currents localized at the boundary [3]. These edge currents are analogous to the (1+1)-dimensional chiral transports, but the coefficients are given by half of theirs. We also discuss the hydrodynamics with more general global anomalies among multiple U(1) symmetries and single Z2 symmetry. References: [1] J.-W. Chen, J.-H. Gao, J. Liu, S. Pu, and Q. Wang, PRD 88, 074003 (2013), [2] N. Poovuttikul, arXiv:2105.13275 [hep-th] (2021), [3] T. Furusawa, M. Hongo, arXiv:2108.12192 [hep-th] (2021). arXiv:2108.12192

## Topological phase, spin Chern-Simons theory and duality on lens space

When: 2021/10/27 (Wed.) 11:00-12:00 Zoom online Shuichi Yokoyama (YITP) I will speak about my recent work of a method to compute topological phase for pure Chern-Simons theory incorporating the supersymmetric localization. We develop a Pauli-Villars regularization preserving supersymmetry and the topological phase appears as a result of the supersymmetric regularization. Applying this method to pure Chern-Simons theory on lens space we compute the background dependent phase factor coming from the Chern-Simons term. We confirm that the partition function computed in this method enjoys a couple of level rank dualities including the one recently proposed by Hsin-Seiberg in arXiv:1607.07457 for all ranks and levels within our numerical calculation. We also present a phase factor with which the lens space partition function exhibits the perfect match between any level rank dual pair including the total phase. If time permits, I will comment on this perfect match of the lens space partition function including the total phase for a couple of Seiberg duality pairs including the matter contribution. This talk is based on arXiv:2108.09300, joint-work with Naotaka Kubo in YITP. arXiv:2108.09300

## Fermi-gas correlators of ADHM theory and triality symmetry

When: 2021/10/22 (Fri.) 12:30-13:30 Zoom online Yasuyuki Hatsuda (Rikkyo Univ.) We analytically study the Fermi-gas formulation of sphere correlation functions of the Coulomb branch operators for 3d N=4 ADHM theory with a gauge group U(N). We find that the leading coefficients of the perturbative grand canonical correlation functions are invariant under a hidden triality symmetry conjectured from the twisted M-theory. The triality symmetry also helps us to fix the next-to-leading corrections analytically. arXiv:2107.01924

## Four-dimensional N=1 theories, S-folds, T-branes, and behaviors in IR and UV

When: 2021/08/04 (Wed.) 11:00-12:00 Honkan (Main Bldg.) H2-39 Yusuke Kimura (KEK) We analyze four-dimensional (4d) N=1 superconformal field theories (SCFTs) obtained as deformations of 4d N=2 SCFTs on S-folds by tilting 7-branes. We discuss that geometric compatibility with the structures of S-folds constrains the forms of T-branes. We also discuss two 4d N=1 theories on probe D3-branes, where the two theories behave identically in IR, but they originate from different theories in UV. Studying the global structure of their geometry is useful in constructing these two theories. arXiv:2011.04460

## Evaporation of black holes in flat space entangled with an auxiliary universe

When: 2021/07/21 (Wed.) 11:00-12:00 Zoom online Akihiro Miyata (Tokyo Univ., Komaba) We study a thermofield double type entangled state on two disjoint universes, where one of the universes is asymptotically flat containing a black hole and the other is non-gravitating. The entanglement between the two disjoint universes effects the geometry of the black hole through the stress energy tensor, and the deformed geometry has a similar structure to an evaporating black hole in flat space. We then compute the entanglement entropy of the non-gravitating universe by using island formula and check that it naturally follows the Page curve of an evaporating black hole in flat space. We also study the effect of a local quench in the universe which contains the black hole and find that the local quench accelerates the evaporation of the black hole. arXiv:2104.00183