Kyushu IAS-iTHEMS conference: Non-perturbative methods in QFT

10 Mar 2025, 09:00 → 14 Mar 2025, 18:00 Asia/Tokyo

Inamori Center (Kyushu University Institute for Advanced Study)

Overview

The most commonly used approach in the study of QFT is perturbation theory. Indeed, we have succeeded in extracting various physical quantities from perturbative (asymptotic) expansions. However, some physical phenomena cannot be captured through perturbative analyses alone. How can we extract these non-perturbative effects?

In QFTs with conformal symmetry (i.e., CFTs), correlation functions can be computed using a method called the conformal bootstrap. This non-perturbative method differs entirely from the usual correlation function analysis methods of QFT, as it does not even assume the existence of a Lagrangian. Through the use of the conformal bootstrap, we have actually made significant progress in the non-perturbative understanding of CFTs.

Furthermore, according to the holographic principle, CFTs provide a non-perturbative formulation of QFTs with gravity (i.e., quantum gravity). By applying the holographic principle to various non-perturbative results from CFTs, such as those obtained from the conformal bootstrap, we have made remarkable advances in understanding the non-perturbative aspects of quantum gravity. Conversely, the holographic principle is also used to understand properties of QFTs that are difficult to analyze perturbatively, through gravity.

Another frequently used approach for understanding non-perturbative aspects involves the use of interfaces. Although there are various ways to apply interfaces, some examples include:

• Symmetry,
• Non-local probes (such as Wilson lines or entanglement entropy),
• RG interfaces (used as a tool to understand the UV/IR map).

Regarding the first point, the relation “symmetry ⇒ topological interface” is well-known, but in general, topological interfaces do not have a group structure, so the reverse does not hold. However, it has recently been recognized that even topological interfaces without group structures can be as powerful as symmetry (sometimes called "generalized symmetry"), and there has been a dramatic development in understanding the properties and applications of topological interfaces in recent years.

The purpose of this conference is to bring together experts who have contributed to the recent advancements in non-perturbative methods of QFTs, to generate new collaboration research from the multifaceted perspective.

In this conference, we plan to cover the following topics, though we welcome any experts on non-perturbative analysis methods beyond these:

• Bootstrap,
• Non-local operator,
  • topological interface = generalized symmetry,
  • non-topological interface, generalized fusion
  • RG flow/interface,
  • boundary
• Holography (understanding non-perturbative aspects from one side to the other).

 

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Invited Speakers

 

Research talks (* to be confirmed):

• Nathan Benjamin (USC)
• Yichul Choi (IAS)
• Justin Kaidi (Kyushu U.)
• Shota Komatsu (CERN)
• Marco Meineri (U. Turin)
• Yu Nakayama (YITP)
• Tatsuma Nishioka (Osaka U.) ⇒ Dongsheng Ge (Osaka U.)
• Ingo Runkel (Hamburg U.)
• Tadashi Takayanagi (YITP)
• Yifan Wang (NYU)
• Yang Zhou (Fudan U.)

 

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Schedule

 

To view the abstract for invited talks or short talks, click "View contribution details" on the Timetable, as shown in the figure below. If you open the contribution details for a short talk, a list of subcontributions will appear, allowing you to view the abstract for each short talk.

 

 

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Registration information

We will have some short talk slots.

There will also be a poster session and we encourage students and young postdocs to present a poster.

The registration deadline will be

01/10/2025 (Fri).

If you need a visa, you may need to register early.

We will provide the support of local expenses for a limited number of young postdocs and students who give a presentation. If you wish to request the support, early registration is required.

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Acknowledgment

We will be grateful if you acknowledge this workshop in a paper initiated or conducted during this workshop. Here is a sample of acknowledgments:

• The authors thank Kyushu University Institute for Advanced Study and RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program. Discussions during the "Kyushu IAS-iTHEMS workshop: Non-perturbative methods in QFT" were useful in completing this work.
   

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Organizers

• Yuya Kusuki (Kyushu University)
• Masazumi Honda (RIKEN iTHEMS)
• Hiroshi Suzuki (Kyushu University)
• Tsukasa Tada (RIKEN iTHEMS)
• Osamu Fukushima (RIKEN iTHEMS)
• Hajime Otsuka (Kyushu University)
• Okuto Morikawa (RIKEN iTHEMS)

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Supporting Organizations

This conference is supported by Kyushu University Institute for Advanced Study, RIKEN iTHEMS, KAKENHI.

 

 

 

 

 

 

Monday 10 March

1 Angular fractals in thermal CFT

I will discuss universal properties of partition functions at high temperature and large angular fugacity in d>2 conformal field theories (CFTs). This provides spin-refined information -- namely the statistics of spins of local operators -- valid for all CFTs, that in some sense generalizes modular invariance of d=2 CFTs. As an example application, I will show that the effective free energy of even-spin minus odd-spin operators at high temperature is smaller than the usual free energy by a factor of 1/2^d.

Speaker: Nathan Benjamin (USC)

Nathan.pdf

11:00 Coffee break

2 Short talks

12:30 Lunch

3 Taming Asymptotic Freedom with Anti-de-Sitter

Anti-de-Sitter space acts as an infra-red cut off for asymptotically free theories, allowing interpolation between a weakly-coupled small-sized regime and a strongly-coupled flat-space regime. We scrutinize the interpolation for theories in two dimensions from the perspective of boundary conformal theories. We show that the appearance of a singlet marginal operator destabilizes a gapless phase existing at a small size, triggering a boundary renormalization group flow to a gapped phase that smoothly connects to flat space. We conjecture a similar mechanism for confinement in gauge theories.

Speaker: Shota Komatsu (CERN)

Komatsu.pdf

15:00 Coffee break

4 Short talks

Tuesday 11 March

5 Infinitely many new renormalization group flows between Virasoro minimal models from non-invertible symmetries

We discuss the role of non-invertible symmetries in RG flows between
Virasoro minimal models.
They give infinitely many new constraints by generalizing the notion
of anomaly matching to non-invertible symmetries, leading to the
predictions of infinitely many new RG flows.
Our general classification includes the old flows such as
Zamolldchikov's unitary flows, but also all the examples known
including the recent sporadic one e.g. proposed by Klebanov et al.

Speaker: Yu Nakayama (YITP)

Nakayama.pdf

11:00 Coffee break

6 Pinning Defects, Fusion and Factorization

I'll discuss recent results on the dynamics of defects in conformal field theory. In particular, I'll describe the phenomena of defect fusion and the factorization of spacetime under renormalization group flows on defects. I'll illustrate these phenomena with the so-called pinning field defects which have simple definitions in quantum field theory and also comment on the broader implications for understanding extended operators.

Speaker: Yifan Wang (NYU)

Wang.pdf

12:30 Lunch

7 Holographic Entanglement, Pseudo Entropy and Wormholes

The idea of holographic duality in string theory provides a simple
geometric computation of entanglement entropy. This generalizes the celebrated
Bekenstein-Hawking formula of black hole entropy and strongly suggests that a
gravitational spacetime consists of many qubits with quantum entanglement.
Recently, a new extension of entanglement entropy, called pseudo entropy,
which depends on both an initial and a final state, was introduced. This
quantity turned out to have a clear geometric dual via the holography and also
plays a role of a new order parameter of quantum phases. In this talk, after
reviewing the above mentioned developments, we would like to point out that
pseudo entropy becomes a useful probe in traversable wormhole geometries,
where non-hermitian density matrices naturally appear in their CFT duals.

Speaker: Tadashi Takayanagi (YITP)

Takayanagi.pdf

15:00 Coffee break

8 Short talks

Wednesday 12 March

9 Topological symmetries and their gaugings in 2dCFT and 3dTFT

The study of topological defects in quantum field theory has seen a wealth of activity recently leading to many interesting insights, for example the explicit realisation of non-invertible topological defects in higher dimensional QFTs via the gauging of higher form symmetries, or the description of the higher algebraic structures inherent in these topological defects.

In this talk, I would like to focus on low-dimensional examples, where such defects and their properties have been investigated for some time already. I would like to exhibit some of the properties of topological defects in two-dimensional conformal field theory and in three-dimensional topological field theory, and show some of the structural insights into 2dCFT and 3dTFT one can gain with the help of defects. In this way, the well-understood low-dimensional case might serve as a source of ideas and as a test-case for higher dimensional constructions.

Speaker: Ingo Runkel (Hamburg U.)

Runkel.pdf

11:00 Coffee break

10 Short talks

12:30 Lunch

11 No-go theorems for higher-spin charges in AdS_2

Higher-spin conserved currents and charges feature prominently in integrable 2d QFTs in flat space. Motivated by the question of integrable field theories in Anti de-Sitter space, we consider the consequences of higher-spin currents for QFTs in AdS2, and find that their effect is much more constraining than in flat space. Specifically, it is impossible to preserve:(a) any higher-spin charges when deforming a massive free field by interactions, or (b) any spin-4 charges when deforming a CFT by a Virasoro primary. Along the way, we explain how higher-spin charges lead to integer spacing in the spectrum of primaries and constraints on correlation functions.

Speaker: Marco Meineri (U. Turin)

Meineri.pdf

15:00 Coffee break

12 Short talks

Thursday 13 March

13 From Weyl Anomaly to Defect Supersymmetric R\'enyi Entropy and Casimir Energy

We present a closed-form expression for the contribution of surface defects to the supersymmetric Rényi entropy in six-dimensional (2,0) theories. Our results show that this defect contribution is a linear function of 1/n and is directly proportional to 2b-d_2, where b and d_2 are the surface defect Weyl anomaly coefficients. We also derive a closed-form expression for the defect contribution to the supersymmetric Casimir energy, which simplifies to -d_2 (up to a proportionality constant) in the chiral algebra limit. This talk is based on arXiv:2501.09498 with Zixiao Huang and Ma-Ke Yuan.

Speaker: Yang Zhou (Fudan U.)

Zhou.pdf

11:00 Coffee break

14 Short talks

12:30 Lunch

15 Localized RG flows on composite defects and C-theorem

We consider a composite defect system where a lower-dimensional defect (sub-defect) is embedded to a higher-dimensional one, and examine renormalization group (RG) flows localized on the defect. A composite defect is constructed in the (3 − ϵ)-dimensional free O(N) vector model with line and surface interactions by triggering localized RG flows to non-trivial IR fixed points. Focusing on the case where the symmetry group O(N) is broken to a subgroup O(m) × O(N − m) on the line defect, there is an O(N) symmetric fixed point for all N, while two additional O(N) symmetry breaking ones appear for N ≥ 23. We also examine a C-theorem for localized RG flows along the sub-defect and show that the C-theorem holds in our model by perturbative calculations.

Speaker: Dongsheng Ge (Osaka U.)

Ge.pdf

15:00 Coffee break

Poster session

18:30 Banquet

Friday 14 March

16 Non-Invertible Symmetry and Entanglement Entropy

Given a quantum field theory with a global symmetry, it is important to understand how the various observables organize into representations of the symmetry. In this talk, we focus on 2d conformal field theories with non-invertible global symmetries described by fusion categories. We will discuss how the boundary local operators connecting two potentially different conformal boundary conditions organize themselves under the action of non-invertible symmetries, using 3d topological field theory techniques. We then explain how this can be used to compute the sub-leading constant contribution to the non-invertible symmetry-resolved entanglement entropy of a single interval, which is somewhat analogous to the topological entanglement entropy of TQFTs.

Speaker: Yichul Choi (IAS)

Choi.pdf

11:00 Coffee break

17 Short talks

12:30 Lunch

18 Non-Supersymmetric Heterotic Branes

The common statement that any consistent quantum gravity theory contains dynamical objects with all possible charges suggests that there are still a number of hitherto-unidentified branes in string theory. In this talk I will discuss four of these new branes, focusing on heterotic string theories. The talk will cover aspects such as exact worldsheet descriptions of the branes, their relation to ten-dimensional non-supersymmetric heterotic string theories, and connections to the theory of topological modular forms.

Speaker: Justin Kaidi (Kyushu U.)

Kaidi.pdf

15:00 Free discussion