Tadashi Okazaki (Shing-Tung Yau Center of Southeast University)
Abstract:
We define supersymmetric zeta functions and supersymmetric determinants, which can reveal spectral properties complementary to those captured by the supersymmetric indices. They play a crucial role in analyzing the Cardy-like behaviors of the supersymmetric indices and the supersymmetric Casimir energies associated with the supersymmetric partition functions. We investigate a variety of examples of the supersymmetric zeta functions and determinants for two-, four-, and six-dimensional supersymmetric field theories.The talk will be based on the collaborative work https://arxiv.org/abs/2511.22822 with Yu Nakayama.
The anomalies of fermionic systems can have more complicated structures than bosonic systems.
More precisely, the anomalies of two-dimensional bosonic quantum field theories (QFTs) with finite group symmetry G are classified by the ordinary cohomology H^3(G;U(1)),
whereas those of fermionic QFTs are classified by so-called the supercohomology SH(G), which has more layers than H^3(G;U(1)).
This is caused by the fact that the unitary operators supported in disjoint regions can anticommute in fermionic systems, although they are only allowed to commute in bosonic systems.
In this talk, we first review the anomalies in bosonic systems, based on the Hamiltonian formalism (the Else--Nayak method).
We then explain how it is generalized to fermionic systems, and show that we can explicitly write down the fermionic anomalies in the case of U(1) symmetry.
Tadashi Okazaki (Shing-Tung Yau Center of Southeast University)
Abstract:
We define supersymmetric zeta functions and supersymmetric determinants, which can reveal spectral properties complementary to those captured by the supersymmetric indices. They play a crucial role in analyzing the Cardy-like behaviors of the supersymmetric indices and the supersymmetric Casimir energies associated with the supersymmetric partition functions. We investigate a variety of examples of the supersymmetric zeta functions and determinants for two-, four-, and six-dimensional supersymmetric field theories.The talk will be based on the collaborative work https://arxiv.org/abs/2511.22822 with Yu Nakayama.
Two-dimensional quantum field theories with minimal (0,1) supersymmetry have induced interest in recent years. Beyond their mathematical connection to topological modular forms, the dynamical aspects of these theories are also under active investigation. Elliptic genera (or Witten genera), which generalize the Witten index to 2d supersymmetric quantum field theories, encode crucial topological information. They have been instrumental in probing the dynamical properties of 2d SQFTs with two or more supercharges. In this talk, I will explain a formula for the flavored elliptic genus that we recently derived for a class of 2d (0,1) gauged linear sigma models (GLSMs). This result generalizes the earlier work on (0,2) and (2,2) cases by Benini, Eager, Hori, and Tachikawa [1308.4896]. As a validity check, we apply our formula to the family of (0,1) GLSMs proposed by Gukov, Pei, and Putrov in [1910.13455] and verify the triality relationship. This presentation is based on the work [2508.06865] in collaboration with Bao and Yamazaki.
Quantum wormholes, geometric instabilities, and von Neumann algebras
When:
2025/11/12 (Wed.) 16:00-17:00
Where:
Honkan (Main Bldg.) H227B
Speaker:
Ryo Nemoto (Nagoya University)
Abstract:
We entangle heavy 1/2-BPS states in two copies of N = 4 SU(N) Super-Yang-Mills (SYM) theory. Each copy is separately dual to an extremal, supersymmetric, singular black hole geometry (a “superstar”), in which the horizon coincides with a null singularity. General ideas in the AdS/CFT correspondence suggest that the entanglement between the two copies should lead to some form of connectedness between the two geometries (a quantum wormhole).We use von Neumann algebra methods in the SYM theory to diagnose the existence of these wormholes, and demonstrate a relation between the type of the algebra of operators acting on each factor of the entangled state (Type I, II$_{1}$, III$_{\lambda}$, III_{1}) and the presence or absence of instabilities in the associated geometry. We suggest that this relation may generalize beyond the supersymmetric example studied here.
Reference:
Holographic Description of Bulk Wave Packets in AdS_4/CFT_3
When:
2025/07/11 (Fri.) 13:30-14:30
Where:
Zoom & Honkan (Main Bldg.) B61
Speaker:
Shiki Yoshikawa (Kyoto University)
Abstract:
In this talk, I will present an extension of the study of wave packets from the AdS_3/CFT_2 correspondence to AdS_4/CFT_3 and examine properties of their energy density. We find that, while the energy still localizes on the light cone, its spatial distribution exhibits momentum dependence and is no longer localized in higher dimensions. This result is significant as it reflects leading 1/N corrections to the generalized free field theory associated with the free bulk theory at N = ∞. Our findings are consistent with previous studies on entanglement wedge reconstruction including 1/N corrections, and also provide new insights into the structure of wave packets in higher-dimensional holography. If time permits, I will also briefly discuss ongoing work on applying this framework to black hole geometries, where thermal and dissipative effects become relevant.
Large Landscape of 4d Superconformal Field Theories from Small Gauge Theories
When:
2025/06/25 (Wed.) 16:00-17:00
Where:
Honkan (Main Bldg.) H227B
Speaker:
Kazunobu Maruyoshi (Seikei University)
Abstract:
We systematically explore the space of renormalization group flows of four-dimensional N=1 superconformal field theories (SCFTs) triggered by relevant deformations, as well as by coupling to free chiral multiplets with relevant operators. In this way, we classify all possible fixed point SCFTs that can be obtained from certain rank 1 and 2 supersymmetric gauge theories with small amount of matter multiplets, identifying 7,346 inequivalent fixed points which pass a series of non-trivial consistency checks. This set of fixed points exhibits interesting statistical behaviors, including a narrow distribution of central charges (a,c), a correlation between the number of relevant operators and the ratio a/c, and trends in the lightest operator dimension versus a/c. The ratio a/c of this set is distributed between 0.7228 and 1.2100, where the upper bound is larger than that of previously known interacting SCFTs. Moreover, we find a plethora of highly non-perturbative phenomena, such as (super)symmetry enhancements, operator decoupling, non-commuting renormalization group flows, and dualities. We especially identify amongst these fixed points a new SCFT that has smaller central charges (a,c)=(633/2000, 683/2000) than that of the deformed minimal Argyres-Douglas theory, as well as novel Lagrangian duals for certain N=1 deformed Argyres-Douglas theories. We provide a website https://qft.kaist.ac.kr/landscape/ to navigate through our set of fixed points. This talk is based on the papers arXiv:2408.02953 and arXiv:1806.08353, collaboration with Minseok Cho, Emily Nardoni and Jaewon Song.
In this talk, I will present how the exact WKB framework can be applied to Floquet systems, i.e. periodically driven two-level quantum systems. Our approach offers a systematic treatment of the low-frequency regime, where conventional Floquet-Magnus expansions fail. By writing the quasi-energies and the effective Floquet Hamiltonian in terms of Voros-type cycle integrals, we capture both the perturbative and the crucial non-perturbative (exponentially small) corrections controlling resonant oscillations between the two levels that occur at specific frequencies. The resulting analytic expressions shows an excellent agreement with numerical simulations and remain reliable even at strongly resonant points.
Holographic Entanglement Entropy in the FLRW Universe
When:
2025/05/23 (Fri.) 13:30-14:30
Where:
Honkan (Main Bldg.) B61
Speaker:
Toshifumi Noumi (University of Tokyo)
Abstract:
We discuss properties of the holographic entanglement entropy in the three-dimensional Friedmann--Lemaitre--Robertson--Walker universe. We consider two types of holographic scenarios analogous to the static patch holography and the half de Sitter holography, in which the holographic boundary is timelike and placed in the bulk. We find in general that the strong subadditivity can be satisfied only in the former type and in addition the holographic boundary has to fit inside the apparent horizon. Also, for the universe filled with an ideal fluid of constant equation of state w < −1, the condition is sharpened as that the holographic boundary has to fit inside the event horizon instead. These conditions provide a necessary condition for the dual quantum field theory to be standard and compatible with the strong subadditivity.
We compute observables in the interacting rank-one 6d N=(2, 0) SCFT at large R-charge. We focus on correlators involving \Phi^n, namely symmetric products of the bottom component of the supermultiplet containing the stress-tensor. By using the moduli space effective action and methods from the large-charge expansion, we compute the OPE coefficients in an expansion in 1/n. The coefficients of the expansion are only partially determined from the 6d perspective, but we manage to fix them order-by-order in 1/n numerically by utilizing the 6d/2d correspondence. This is made possible by the fact that this observable can be extracted in 2d from a specific double-scaling limit of the vacuum Virasoro block, which can be efficiently computed numerically. We also extend the computation to higher-rank SCFTs, and discuss various applications of our results to 6d as well as 2d.
Higgsing procedure of line defect half-indices in N=4 SYM theories
When:
2025/04/25 (Fri.) 13:30-14:30
Where:
Honkan (Main Bldg.) B61
Speaker:
Tadashi Okazaki (Southeast University)
Abstract:
We demonstrate that the line defect half-indices of the ’t Hooft lines of magnetic charges corresponding to the minuscule representations in the presence of the Nahm pole boundary conditions can be obtained by applying the Higgsing prescription to the half-indices of the Dirichlet boundary conditions. Accordingly, we find precise matching of the indices for pairs of the S-dual configurations with the Wilson lines and Neumann boundary conditions and those with the ’t Hooft lines and Nahm pole boundary conditions.
The Schur index in four-dimensional N=4 super Yang-Mills theory with U(N) gauge group has a natural two-parameter deformation. We find that a matrix integral in such a deformed Schur index can be exactly evaluated by using Macdonald polynomials. The resulting expression is a simple combinatorial summation over partitions. An extension to line operator indices is straightforward. In particular, for an anti-symmetric representation, the line operator index has a relatively simple form. We further discuss infinite N analysis and finite N giant graviton expansions.
Exploring Complex Saddles and Geometries through Holography
When:
2025/03/10 (Mon.) 13:30-14:30
Where:
Honkan (Main Bldg.) H227C
Speaker:
Heng-Yu Chen (National Taiwan University)
Abstract:
Studying gravitational path integral often leads one to encounter complex saddles and the corresponding geometries, some may have interesting physical interpretations while others may be unphysical, it is therefore interesting to study them through the lens of holography. In this talk, I will report some recent progresses in this direction by applying holography correspondence for both asymptotically Anti de-Sitter and de-Sitter spacetimes. We employ the suitable analytic continuations of dual CFT correlation functions, the method of mini-superspace, and resurgence to explore these complex saddles. In the process we will provide the geometric interpretations for them, which are consistent with the holography correspondences. The work was done in collaborations with Yasuaki Hikida, Yusuke Taki and Takahiro Uetoko.
Reference:
Giant Gravitons and Volume Minimisation
When:
2025/02/21 (Fri.) 13:30-14:30
Where:
Honkan (Main Bldg.) 227B
Speaker:
Sanefumi Moriyama (Osaka Metropolitan University)
Abstract:
The giant graviton expansion of the superconformal index of field theories and the master volume in volume minimization exhibit notable similarities. In our recent work, we establish a precise correspondence between these two concepts. In this talk, I will explain this correspondence and discuss its consistency with the simple sum reduction and the parallelogram ansatz.
Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
When:
2025/01/29 (Wed.) 16:00-17:00
Where:
Zoom Online
Speaker:
Zengo Tsuboi ()
Abstract:
We derive QQ-relations (functional relations among Baxter Q-functions) and T-functions (eigenvalues of transfer matrices) for fusion vertex models associated with twisted quantum affine superalgebras and untwisted quantum affine orthosymplectic superalgebras (and their Yangian counterparts) as reductions (a kind of folding) of those associated with the quantum affine general linear superalgebra $U_{q}(gl(M|N)^{(1)})$. In particular, we reproduce previously proposed generating functions (difference operators) of the T-functions for the symmetric or anti-symmetric representations, and tableau sum expressions for more general representations for orthosymplectic superalgebras, and obtain Wronskian-type expressions (analogues of Weyl-type character formulas) for them. T-functions for spinorial representations are related to reductions of those for asymptotic limits of typical representations of $U_{q}(gl(M|N)^{(1)})$.
Genus 2 Superstring Chiral Measure From The 3-Dimensional Gelca-Hamilton TQFT
When:
2025/01/22 (Wed.) 16:00-17:00
Where:
Zoom & Honkan (Main Bldg.) H227B
Speaker:
Saki Koizumi (DIAS)
Abstract:
In the path integral formulation of the superstring, the chiral measure acquires a phase under the modular transformation of a Riemann surface.
This motivated the use of anomaly inflow to define the superstring chiral measure by a path integral formalism of a modular invariant $3$-dimensional theory.
A Gelca-Hamilton topological field theory (TQFT) is one of the Atiyah’s TQFT on a $3$-dimensional extended manifold with the boundary Jacobi variety of a Riemann surface, whose Hilbert space is spanned by the theta series.
We show that genus $g\leq 2$ superstring chiral measure in the path integral can be obtained by the path integral of the Gelca-Hamilton TQFT on some $3$-dimensional bulk extended manifolds.
The modular transformation of the superstring chiral measure can be understood as the action of the extended mapping class group on the bulk $3$-dimensional extended manifolds.
Heterotic string theory has nonsupersymmetric branes whose existence is suggested by the cobordism conjecture. We numerically construct static, spherically symmetric and asymptotically flat black brane solutions in ten dimensional heterotic string theories for 0- and 4-branes. These branes carry charges that are measured by Chern classes on the sphere surrounding the branes. For the extremal case, the solution have a throat region with a linear dilaton profile as expected from the corresponding world sheet theory. We also construct non-extremal solutions by compactifying the time direction. To verify the reliability of our numerical calculations, we confirm that they reproduce the known analytical solutions for the 6-brane. Our black brane solutions provide evidence supporting the existence of such branes in heterotic string theory. In this talk, I will explain our motivation for constructing these solutions in heterotic string theory, and then discuss how to realize them.
Gauge origami is a generalized supersymmetric quiver gauge theory where intersecting D-branes appear. The simplest setup is the gauge origami system in $\mathbb{C}^4$, where D2/D4/D6/D8 branes are present. Instantons are D0-branes bound to the D(2p)-branes, and the partition functions are the flavored Witten indices of the supersymmetric quantum mechanics of the D0-branes. We demonstrate that the contour integral formulas of the partition functions have free field interpretations, leading to the operator formalism of $qq$-characters, which we generally call BPS $qq$-characters. On one hand, the $qq$-characters of D2-D0 and D4-D0 bound states correspond to screening charges and generators of the affine quiver W-algebra, respectively. On the other hand, the $qq$-characters of D6-D0 and D8-D0 bound states give new types of $qq$-characters, where the monomial terms are characterized by plane partitions and solid partitions. The D4, D6, D8 $qq$-characters automatically reproduce the partition function of the spiked instanton, tetrahedron instanton, and the magnificent four, which eventually establish the BPS/CFT correspondence. We also discuss the relation with quantum toroidal algebras and generalizations to toric Calabi-Yau four-folds. This talk is based on arXiv: 2310.08545, 2404.17061, 2411.01987
Hawking-Page and entanglement phase transition in 2d CFT on curved backgrounds
When:
2024/12/11 (Wed.) 16:00-17:00
Where:
Zoom
Speaker:
Akihiro Miyata (YITP)
Abstract:
The thermodynamics and the entanglement properties of two-dimensional conformal field theories (2d CFTs) on curved backgrounds are studied. By means of conformal mapping we study the equivalent system on flat space governed by the deformed Hamiltonian, which is a spatial integral of the Hamiltonian density modulated by an enveloping function. Focusing on holographic CFTs, we observe Hawking-Page like phase transition for the thermal and the entanglement entropy as we vary the background metric. We also compute the mutual information to study the information theoretic correlation between parts of the curved spacetime. The gravity dual of 2d CFTs on curved background is also discussed.
This presentation is based on the paper, A. Miyata, M. Nozaki, K. Tamaoka, and M. Watanabe, JHEP 08 (2024) 190. [arXiv: 2406.06121]
A concrete construction of topological operator in factorization algebras
When:
2024/11/13 (Wed.) 16:00-17:00
Where:
Honkan (Main Bldg.) H227B
Speaker:
Masashi Kawahira (YITP)
Abstract:
In this talk, we will discuss a concrete construction of a topological operator in factorization algebras. Factorization algebras play an important role in modern mathematics and physics in the formulation of quantum field theories by K. Costello and his collaborators. We will provide a definition of topological operators and a construction of the topological operator corresponding to shift symmetry, in one-dimensional massless scalar field theory.
