# 次回のセミナー (Next Seminar)

## 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

# 最近のセミナー (Recent Seminars)

When: 2022/02/02 (Wed.) 11:00-14:00 Honkan (Main Bldg.) H2-39 Satoshi Nawata ()

## 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

## Anomaly and Superconnection

When: 2021/07/14 (Wed.) 11:00-12:00 Zoom Hayato Kanno (YITP) We study anomalies of fermion with spacetime dependent mass. We calculate anomalies, which associate with the U(N)×U(N) chiral symmetry for even dimension and U(N) flavor symmetry for odd dimension, using Fujikawa method. We show these anomalies can be written by superconnection. In particular, we focus on vector-like U(1) part of the anomalies in this talk. These results can be applied to some general systems with interfaces and boundaries. They are also useful to some index theorems, such as APS index theorem. In the last part of this talk, the relation between this anomaly and string theory is discussed. This talk is based on [arXiv:2106.01591]. arXiv:2106.01591

## Supersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases

When: 2021/07/07 (Wed.) 11:00-12:00 Zoom online Satoshi Yamaguchi (Osaka University) Fracton phases show exotic properties, such as sub-extensive entropy, local particle-like excitation with restricted mobility, and so on. In order to find natural fermionic fracton phases, we explore supersymmetric quantum field theory with exotic symmetry. We use superfield formalism and write down the action of a supersymmetric version of one of the simplest models with exotic symmetry, the φ theory in 3+1 dimensions. It contains a large number of ground states due to the fermionic higher pole subsystem symmetry. Its residual entropy is proportional to the area instead of the volume. This theory has a self-duality similar to that of the φ theory. We also write down the action of a supersymmetric version of a tensor gauge theory, and discuss BPS fractons. arXiv:2102.04768

## Digital quantum simulation for screening and confinement in gauge theory with a topological term

When: 2021/06/23 (Wed.) 11:00-12:00 Zoom online Lento Nagano (Tokyo Univ.) We perform digital quantum simulation to study screening and confinement in a gauge theory with a topological term, focusing on (1+1)-dimensional quantum electrodynamics (Schwinger model) with a theta term. We compute the ground state energy in the presence of probe charges to estimate the potential between them, via adiabatic state preparation. We compare our simulation results and analytical predictions for a finite volume, finding good agreements. This talk is based on a recent work with M. Honda, E. Itou, Y. Kikuchi, T. Okuda [arXiv:2105.03276]. arXiv:2105.03276

## Oscillating Multiple Giants

When: 2021/06/16 (Wed.) 11:00-12:00 Zoom online Ryo Suzuki (Shing-Tung Yau Center (Southeast University)) Superstring theory on AdS5xS5 has BPS D3-brane states called giant gravitons, which correspond to the operators with huge dimensions in N=4 super Yang-Mills. I discuss the extension of this correspondence to the case of non-BPS multiple giants. On the gauge theory side, we can compute the mixing problem of huge operators by using the restricted Schur polynomials. Under the distant corners approximation, the mixing problem simplifies to the harmonic oscillators of an effective U(p) theory, where p corresponds to the number of giant gravitons. By requiring the commutations of the perturbative dilatation operators, I propose an all-loop ansatz for the anomalous dimensions, which suggests that the excitation spectrum is gapless. On the string theory side, I solve the classical equations of motion for the non-maximal giant graviton perturbatively, finding qualitative agreement with the all-loop proposal. arXiv:2101.05310

## Quantum phase transition and Resurgence: Lessons from 3d N=4 SQED

When: 2021/06/09 (Wed.) 11:00-12:00 Zoom online Takuya Yoda (Kyoto Univ.) We study a resurgence structure of a quantum field theory with a phase transition to uncover relations between resurgence and phase transitions. In particular, we focus on three-dimensional N=4 supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has been recently proposed in the large-flavor limit. We provide interpretations of the phase transition from the viewpoints of Lefschetz thimbles and resurgence. For this purpose, we study the Lefschetz thimble structure and properties of the large-flavor expansion for the partition function obtained by the supersymmetric localization. We show that the second-order phase transition is understood as a phenomenon where a Stokes and anti-Stokes phenomenon occurs simultaneously. The order of the phase transition is determined by how saddles collide at the critical point. In addition, the phase transition accompanies an infinite number of Stokes phenomena due to the supersymmetry. These features are appropriately mapped to the Borel plane structures as the resurgence theory expects. Given the lessons from the SQED, we provide a more general discussion on the relationship between the resurgence and phase transitions. In particular, we show how the information on the phase transition is decoded from the Borel resummation technique. arXiv:2103.13654

## Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on S1

When: 2021/06/02 (Wed.) 11:00-12:00 Zoom online Naohisa Sueishi (Keio Univ.) We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with N minima on S1. We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks, and provide a dictionary between the two. The two formulations are equivalent, but with their own pros and cons. Exact-WKB produces the quantization condition consistent with the known conjectures and mixed anomaly. The quantization condition for the case of N-minima on the circle factorizes over the Hilbert sub-spaces labeled by discrete theta angle (or Bloch momenta), and is consistent with 't Hooft anomaly for even N and global inconsistency for odd N. By using Delabaere-Dillinger-Pham formula, we prove that the resurgent structure is closed in these Hilbert subspaces, built on discrete theta vacua, and by a transformation, this implies that fixed topological sectors (columns of resurgence triangle) are also closed under resurgence. arXiv:2103.06586

## Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries

When: 2021/05/26 (Wed.) 11:00-12:00 Zoom online Yuji Sugimoto (CUST) In this talk, I will explain the relation between topological string theories on toric Calabi—Yau manifolds and integrable systems. More concretely, I will explain the quantization of the genus-2 mirror curves which are related to the dimer models. This enables us to calculate the spectra of the dimer models from the topological strings. In order to calculate the spectra, we use the differential operators which are usually used to calculate the quantum corrections to the mirror maps and derivatives of the prepotential. Through the analysis, we observe that the differential operators do not depend on the choice of the cycles. arXiv:2006.13482

## Some comments on 6d global gauge anomalies

When: 2021/05/19 (Wed.) 11:00-12:00 Zoom online Yasunori Lee (Tokyo Univ.) Given a G gauge theory, there can be global (non-perturbative) gauge transformations under which the partition function is not invariant. In 6d, relevant cases include G = SU(2), SU(3), and G_2, and the old computations utilizing homotopy groups affirmed that the anomalous phases can indeed arise in all three cases. On the other hand, from the modern point of view utilizing bordism groups, there should not be such global gauge anomalies in the first place. In this talk, I will describe how this apparent conflict is resolved by carefully examining the cancellation of perturbative gauge anomalies via 6d Green-Schwarz mechanism. arXiv:2012.11622

## Non-perturbative tests of duality cascades in three-dimensional supersymmetric gauge theories

When: 2021/04/21 (Wed.) 16:00-17:00 Zoom Naotaka Kubo (YITP) We study the RG flow of three-dimensional ${\cal N}=3$ supersymmetric Yang-Mills-Chern-Simons theories described by circular quiver diagrams. When the gauge group is $U(N)\times U(N+M)$ and $M$ is larger than the Chern-Simons level, a duality cascade, which is a sequence of the Seiberg-like dualities, was expected to occur. It was also predicted that sometimes the supersymmetry would be dynamically broken. These properties can be fully captured by the braneology: the Hanany-Witten transitions and the $s$-rule. Based on this fact, we conjecture that the theories described by the general circular quiver diagrams also have similar properties. We test this prediction by using the partition function on $S^3$. The results are in agreement with our prediction. arXiv:2010.15656