Name: YITP-IAS (Kyushu Univ.) workshop: Interfaces & Symmetry
Start: 2026-03-02T09:00:00+09:00
End: 2026-03-06T17:00:00+09:00
Location: Yukawa Institute for Theoretical Physics, Kyoto University

YITP-IAS (Kyushu Univ.) workshop: Interfaces & Symmetry

from Monday, March 2, 2026 (9:00 AM) to Friday, March 6, 2026 (5:00 PM)

Monday, March 2, 2026

9:25 AM Opening
Opening
9:25 AM - 9:30 AM
Room: Maskawa Hall
9:30 AM Permutation defects and multi entropy measures for topologically ordered states - Shinsei Ryu (Princeton University)
Permutation defects and multi entropy measures for topologically ordered states
- Shinsei Ryu (Princeton University)
9:30 AM - 10:30 AM
Room: Maskawa Hall Entanglement entropy has long served as a key diagnostic of topological order in (2+1) dimensions. In particular, the topological entanglement entropy captures a universal quantity (the total quantum dimension) of the underlying topological order. However, this information alone does not uniquely determine which topological order is realized, indicating the need for more refined probes. In this talk, I will present a family of quantities formulated as multi-entropy measures, including examples such as reflected entropy and the modular commutator. Unlike the conventional bipartite setting of topological entanglement entropy, these multi-entropy measures are defined for tripartite partitions of the Hilbert space and capture genuinely multipartite entanglement. I will discuss how these measures encode additional universal data characterizing topologically ordered ground states.
10:30 AM Coffee break
Coffee break
10:30 AM - 11:00 AM
Room: Maskawa Hall
11:00 AM When can two QFTs be separated by a topological interface? - Brandon Rayhaun (YITP, Stony Brook)
When can two QFTs be separated by a topological interface?
- Brandon Rayhaun (YITP, Stony Brook)
11:00 AM - 12:00 PM
Room: Maskawa Hall I will discuss the question posed in the title in the context of 2D CFTs. In particular, I will conjecture and provide some evidence that the answer is “always” if the two CFTs have the same left- and right-moving central charges, so long as one accepts topological interfaces of infinite quantum dimension. I will also illustrate how a topological interface between Theory A and Theory B allows one to transport knowledge about Theory A (its spectrum, its category of boundary conditions, its topological lines, etc.) to Theory B. Finally, I will explain some tiny miracles which make these ideas really come to life on the c=1 conformal manifold, and foreshadow a program wherein one completely solves c=1 conformal field theory in terms of the SU(2)1 WZW model. The talk is based on various projects with Yichul Choi and Ho Tat Lam, with Terry Gannon, and with Sven Möller.
12:00 PM Lunch
Lunch
12:00 PM - 2:00 PM
Room: Maskawa Hall
2:00 PM Analytic bootstrap for holographic surface defects - Lorenzo Bianchi (Turin U.)
Analytic bootstrap for holographic surface defects
- Lorenzo Bianchi (Turin U.)
2:00 PM - 3:00 PM
Room: Maskawa Hall In this talk I will review the recent developments in the application of analytic bootstrap techniques to defect conformal field theories. I will briefly outline some applications and then I will focus on 1/2 BPS surface defects in N=4 SYM theory (the most notable example being Gukov Witten defects). I will show how analytic bootstrap tools can be used to compute the holographic bulk two-point function.
3:00 PM Coffee break
Coffee break
3:00 PM - 3:30 PM
Room: Maskawa Hall
3:30 PM Accurate boundary bootstrap for the 3d O(N) normal universality class - Wenliang Li
Accurate boundary bootstrap for the 3d O(N) normal universality class
- Wenliang Li
3:30 PM - 4:00 PM
Room: Maskawa Hall The three-dimensional classical O(N) model with a boundary has received renewed interest due to the discovery of the extraordinary-log boundary universality class for 2≤N<Nc. The critical value Nc and the exponent of the boundary correlation function are related to certain amplitudes in the normal universality class. To determine their precise values, we revisit the 3d O(N) boundary conformal field theory for N=1,2,3,4,5. After substantially improving the accuracy of the boundary bootstrap, our determinations are in excellent agreement with the Monte Carlo results, resolving the previous discrepancies due to low truncation orders. We also use the recent bulk bootstrap results to deduce highly accurate Ising data. Many bulk and boundary predictions are obtained for the first time. Our results demonstrate the great potential of the η minimization method for many unexplored bootstrap problems in which positivity constraints are absent.
4:00 PM Multipoint Lightcone Bootstrap with a defect - Lorenzo Quintavalle (University of Torino)
Multipoint Lightcone Bootstrap with a defect
- Lorenzo Quintavalle (University of Torino)
4:00 PM - 4:30 PM
Room: Maskawa Hall It is a well-established fact that any conformal field theory with a gap in the twist spectrum must contain families of multi-twist operators, whose spectrum at large spin approaches that of generalized free theory. In presence of a defect, this statement gets enriched by the existence of families of defect operators known as transverse derivative operators. In this talk, we aim to discuss how the lightcone bootstrap can be applied to defect correlation functions with more than two field insertions to extract new dynamical data at large transverse spin that was previously out of reach.
4:30 PM Haagerup Symmetry in (E_8)_1 - Yamato Honda (Kyushu U.)
Haagerup Symmetry in (E_8)_1
- Yamato Honda (Kyushu U.)
4:30 PM - 5:00 PM
Room: Maskawa Hall In this talk, I will explain that the (E_8)_1 WZW model has Haagerup symmetry H_3, and that gauging H_3 gives a c = 8 theory with Z(H_3) symmetry. In addition, I will suggest a relation to theories with H_3 symmetry at c = 2 and c = 6, complementing the discussion with new modular bootstrap results.
Tuesday, March 3, 2026
9:30 AM From Phases to Phase-Gates - Sakura Schafer-Nameki (Oxford University)
From Phases to Phase-Gates
- Sakura Schafer-Nameki (Oxford University)
9:30 AM - 10:30 AM
Room: Maskawa Hall I will give an overview of recent developments using the Symmetry TFT to characterize phases of matter with categorical symmetries, which turns out to have a very curious, and potentially far-reaching implication in the construction of universal quantum computation in 2D lattice models -- namely the construction of transversal phase gates. This gives a surprising connection between advances in classification of phases on the one hand and applications in quantum computation.
10:30 AM Coffee break
Coffee break
10:30 AM - 11:00 AM
Room: Maskawa Hall
11:00 AM Arf–Brown–Kervaire Invariant on the Lattice - Satoshi Yamaguchi (Osaka U.)
Arf–Brown–Kervaire Invariant on the Lattice
- Satoshi Yamaguchi (Osaka U.)
11:00 AM - 12:00 PM
Room: Maskawa Hall Lattice field theory provides one of the most reliable nonperturbative regularizations of quantum field theory. Meanwhile, the eta invariant of the Dirac operator, defined as a regularized sum of the signs of its eigenvalues, plays an important role in symmetry-protected topological phases and in anomalies in quantum field theories. In this talk, we investigate how the eta invariant can be formulated within lattice field theory. In particular, we construct a lattice formulation of the Arf–Brown–Kervaire (ABK) invariant in two dimensions. Domain walls, or interfaces, are useful tools for studying the ABK invariant on surfaces with boundaries.
12:00 PM Lunch
Lunch
12:00 PM - 2:00 PM
Room: Maskawa Hall
2:00 PM Cosmic string for electromagnetic duality - Shu-Heng Shao (MIT)
Cosmic string for electromagnetic duality
- Shu-Heng Shao (MIT)
2:00 PM - 3:00 PM
Room: Maskawa Hall We study novel conformal twist defects in 4d Maxwell theory, around which electric and magnetic fields are exchanged. These are codimension-2 defects living at the end of topological defects for certain non-invertible global symmetries. We determine the operator spectrum of the twist defect by solving classical electromagnetic wave equations subject to a twisted boundary condition. Using techniques from defect CFT, we show that correlation functions of these defect operators factorize into two sectors: a universal generalized free-field sector, and a chiral current sector analogous to edge modes in ChernSimons theory.
3:00 PM Coffee break
Coffee break
3:00 PM - 3:30 PM
Room: Maskawa Hall
3:30 PM The Effective Field Theory of Fluctuating Defects - Thekla Lepper (Università di Torino)
The Effective Field Theory of Fluctuating Defects
- Thekla Lepper (Università di Torino)
3:30 PM - 4:00 PM
Room: Maskawa Hall Defect conformal field theories (DCFTs) provide a universal framework for describing the low energy interaction of heavy degrees of freedom with light excitations. In a DCFT part of the Poincaré symmetry is broken explicitly. However, the fundamental laws of our world are Poincaré invariant and any breaking of space-time symmetries must be spontaneous. In particular, extended and thin objets which spontaneously break Poincaré invariance support the propagation of Goldstone bosons on their worldvolume. Their action is invariant under a non-linear realization of the Poincaré symmetry. Since the Goldstone bosons are massless, a natural question is, how DCFTs can describe the infrared limit of real-world heavy objects embedded in a massless bulk. The work I am going to present aims to answer this question by constructing an effective field theory that describes the coupling of the Goldstone bosons to a generic DCFT.
4:00 PM Subdimensional Disorder and Logarithmic Defect - Soichiro Shimamori (Osaka U.)
Subdimensional Disorder and Logarithmic Defect
- Soichiro Shimamori (Osaka U.)
4:00 PM - 4:30 PM
Room: Maskawa Hall We study quenched disorder localized on a p-dimensional subspacetime in a d-dimensional conformal field theory. Motivated by the logarithmic behavior often associated with disorder, we introduce a defect setup in which bulk local operators transform in ordinary conformal representations, while defect local operators assemble into logarithmic multiplets. We refer to such objects as logarithmic defects and investigate their model-independent properties dictated solely by conformal symmetry and its representation theory, including correlation functions, logarithmic defect operator expansions, and conformal blocks. As a concrete ex- ample, we analyze the free scalar theory with a generalized pinning defect subject to random coupling fluctuations, and we identify a half-line of fixed points describing the corresponding logarithmic conformal defects. Along the way, we propose a candidate monotone governing defect renormalization group flows induced by subdimensional disorder. We comment on various generalizations and the broader program of bootstrapping logarithmic defects. This talk is based on the collaboration with Yifan Wang (New York University) [hep-th: 2510.13964].
4:30 PM Comparing top-down and bottom-up holographic defects and boundaries - William Bradford Harvey (University of Victoria)
Comparing top-down and bottom-up holographic defects and boundaries
- William Bradford Harvey (University of Victoria)
4:30 PM - 5:00 PM
Room: Maskawa Hall In this talk, I will consider "bottom-up" (toy) models of Einstein gravity with either gravitating domain walls or end-of-the-world (ETW) branes. In AdS/CFT language, these bulk objects are holographically dual to codimension-one conformal defects and boundaries, respectively. Depending on which type of model, one can study notions of either an AdS/DCFT or an AdS/BCFT correspondence. From here, in lieu of strictly working with "top-down constructions", i.e., proper 10- or 11-dimensional supersymmetric string theories with known holographic duals, one may wish to utilize the simpler bottom-up models (when possible) when exploring various aspects of holography. My goal in this talk is to address this desire indirectly by exploring the viability of the bottom-up models, which I will primarily do by comparing the bottom-up models' precision with results obtained from known top-down constructions. The physical quantities we compare are the holographic defect/boundary entanglement entropies (presumed to exist for the bottom-up models), which are interpreted through a shared quantity known as "\phi_{b}" which itself has both a bulk and boundary interpretation. In the bulk, \phi_{b} is the proper time of a geodesic null trajectory in the bulk from the conformal boundary to the domain-wall/ETW brane and back. In a dual boundary theory, \phi_{b} marks an (unexpected) seemingly apparent singularity in boundary correlators. The results of this analysis will be organized according to type of holographic dual, i.e. defect theories and boundary theories, respectively.
Wednesday, March 4, 2026
9:30 AM TBA - Michele Del Zotto (Uppsala U.)
TBA
- Michele Del Zotto (Uppsala U.)
9:30 AM - 10:30 AM
Room: Maskawa Hall
10:30 AM Coffee break
Coffee break
10:30 AM - 11:00 AM
Room: Maskawa Hall
11:00 AM Defect Anomalies and Scattering Amplitudes - Christian Copetti (Oxford)
Defect Anomalies and Scattering Amplitudes
- Christian Copetti (Oxford)
11:00 AM - 12:00 PM
Room: Maskawa Hall Symmetry can be realized in an anomalous fashion on the dynamical defects of a theory. These "defect anomalies" are exact non-perturbative defect data which constrain their physics in several ways. In this talk, I explain how defect anomalies can be detected in scattering experiments, where they are responsible for processes in which local particles in the in-state are morphed into nonlocal excitations. After giving some introduction about the structure of the -in and -out states in the presence of a defect, I will explain this connection in detail and provide examples. Based on work to appear with A. Antinucci, G. Galati and G. Rizi.
12:00 PM Lunch
Lunch
12:00 PM - 2:00 PM
Room: Maskawa Hall
2:00 PM Interface vs. boundary in the Dirac operator index - Hidenori Fukaya (Osaka U.)
Interface vs. boundary in the Dirac operator index
- Hidenori Fukaya (Osaka U.)
2:00 PM - 2:30 PM
Room: Maskawa Hall We would like to report on our recent study on a mathematical relation between the Atiyah-Patodi-Singer index on a manifold with boundary and the spectral flow on a closed manifold with interfaces. The talk is based on the works in collaboration with S. Aoki, M. Furuta, S. Matsuo, T. Onogi and S. Yamaguchi.
2:30 PM Monopole unitarity puzzle -- Disenchanted - Masataka Watanabe (U. Tokyo)
Monopole unitarity puzzle -- Disenchanted
- Masataka Watanabe (U. Tokyo)
2:30 PM - 3:00 PM
Room: Maskawa Hall In QED coupled to four or more Dirac fermions, the scattering of fermions off a target monopole is exotic; the out state is not in the Fock space one started with. In the s-wave reduced version of the problem, I will describe how one would measure such an out state.
3:00 PM Coffee break
Coffee break
3:00 PM - 3:30 PM
Room: Maskawa Hall

3:30 PM Poster session
Poster session
3:30 PM - 6:00 PM
Room: Maskawa Hall

6:00 PM Banquet
Banquet
6:00 PM - 8:00 PM
Room: Maskawa Hall
Thursday, March 5, 2026
9:30 AM A new universal charge for conformal interfaces - Andreas Karch (UT Austin)
A new universal charge for conformal interfaces
- Andreas Karch (UT Austin)
9:30 AM - 10:30 AM
Room: Maskawa Hall 2d conformal interfaces are thought to be described by a few universal quantities, the boundary entropy, and two central charge like quantities controlling energy and information transport across the interface. We will demonstrate that in the presence of dissipation there is a third universal central charge characterizing the flow of dissipation across the interface. It is universal in that it is insensitive to the microscopic details of the coupling to the environment and only depends on the properties of the interface.
10:30 AM Coffee break
Coffee break
10:30 AM - 11:00 AM
Room: Maskawa Hall
11:00 AM Cusped Impurities: From Casimir Energy to Sudakov Radiation - Gabriel Cuomo (NYU)
Cusped Impurities: From Casimir Energy to Sudakov Radiation
- Gabriel Cuomo (NYU)
11:00 AM - 12:00 PM
Room: Maskawa Hall Cusped line defects play an important role in quantum field theory, with applications ranging from scattering amplitudes to quantum quenches and Casimir-energy computations. In this talk, I will discuss general properties of cusped line defects and, in particular, the cusp anomalous dimension that governs the partition function of a defect with a cusp. After reviewing the Euclidean setting and its connection to defect fusion and Casimir energy, I will turn to the Lorentzian regime and present results for the large-boost-angle (generalized Sudakov) limit.
12:00 PM Lunch
Lunch
12:00 PM - 2:00 PM
Room: Maskawa Hall
2:00 PM When ∃exactly marginal operators - Hirosi Ooguri (Caltech)
When ∃exactly marginal operators
- Hirosi Ooguri (Caltech)
2:00 PM - 3:00 PM
Room: Maskawa Hall
3:00 PM Coffee break
Coffee break
3:00 PM - 3:30 PM
Room: Maskawa Hall
3:30 PM Transmission coefficients from phantom currents - Yuma Furuta (Kyushu U.)
Transmission coefficients from phantom currents
- Yuma Furuta (Kyushu U.)
3:30 PM - 4:00 PM
Room: Maskawa Hall Interfaces in conformal field theory (CFT) appear in many contexts and sometimes play a crucial role in characterizing the theory. For example, topological interfaces have long been studied (such as the name of Verlinde lines) and there exist well-developed methods to extract the information they encode. By contrast, conformal interfaces that are not necessarily topological but conformal, such as RG interfaces, are more complicated and typically much harder to analyze. In this work, we propose a universal method to compute the transmission coefficient associated with a conformal interface between two CFTs that is assumed to be conformal. The key idea is to make use of a spin-2 non-local operator, a “phantom current,” which emerges when folding two theories; under a certain assumption, this allows us to compute the transmission coefficient. In this talk, I will explain this method in detail and discuss its consistency with previously known examples. This talk is based on arXiv:2511.00356.
4:00 PM Conserved defects in deformed 2d CFT - Federico Ambrosino (Perimeter Institute)
Conserved defects in deformed 2d CFT
- Federico Ambrosino (Perimeter Institute)
4:00 PM - 4:30 PM
Room: Maskawa Hall I will present recent advances in the understanding conserved defects in 2d CFTs. Both topological and non-topological defect may give rise to conserved quantities in deformed 2d CFT. I will characterize a class of translational invariant defects from the UV to the IR of an RG flows triggered by relevant perturbation of 2d CFTs. On the way I will discuss various properties of these flows in Minimal models of the WN algebra.
4:30 PM Surface defects and integrability - Adam Chalabi (University of Turin)
Surface defects and integrability
- Adam Chalabi (University of Turin)
4:30 PM - 5:00 PM
Room: Maskawa Hall Integrability of planar N=4 super-Yang-Mills (SYM) theory enables exact computations of unprotected observables, even with the insertion of certain extended operators. While integrability techniques have been successfully applied to some domain walls and line defects, it is an open question whether there are any integrable surface defects in N=4 SYM theory. In this talk, I will examine a class of 1/2-BPS surface defects known as Gukov-Witten defects. I will argue that these defects are generically not integrable but they are likely to become integrable at a corner in parameter space. I will present closed-form factorised expressions for leading-order one-point functions of unprotected scalar operators, hinting at the existence of all-loop formulas at this special point.
Friday, March 6, 2026
9:30 AM Semi-universality of d-dimensional CFT at LARGE spin - Sridip Pal (IHES)
Semi-universality of d-dimensional CFT at LARGE spin
- Sridip Pal (IHES)
9:30 AM - 10:30 AM
Room: Maskawa Hall In unitary 2 dimensional CFT with c>1 and twist gap in Virasoro primaries, modular bootstrap of torus partition function in the light cone limit using rigorous complex analytic method reveals existence of twist accumulation points, and universality of operator spectrum at large spin J: the (appropriately smoothened) density of states is completely universal: theory independent upto J^{-N} for any N>0. In this talk, we will explore this limit in higher dimensional CFT and provide EFT based arguments, along with strong evidence, for what we call “Semi-universality” of spectrum at large spin: the density states at large spin is determined upto a theory-dependent function of universal ratio of twist and spin. The semi-universality has an intriguing connection with ANEC. This will be based on arXiv: 2505.02897 with Balt C van Rees and Jiaxin Qiao & the arXiv: 2512.00158 with Harsh Anand, Nathan Benjamin, Vipul Kumar, Shiraz Minwalla, Jyotirmoy Mukherjee, Asikur Rahaman.
10:30 AM Coffee break
Coffee break
10:30 AM - 11:00 AM
Room: Maskawa Hall
11:00 AM Boundary transitions from a single round of measurements on gapless quantum states - Sara Murciano (Orsay)
Boundary transitions from a single round of measurements on gapless quantum states
- Sara Murciano (Orsay)
11:00 AM - 12:00 PM
Room: Maskawa Hall Measurements can qualitatively alter correlations and entanglement emerging in gapless quantum matter. In this talk, we show how a single round of measurements on gapless quantum systems can, upon rotating the measurement basis, induce non-trivial transitions separating regimes displaying universal characteristics governed by distinct boundary conformal field theories. We develop the theory of such `measurement-induced boundary transitions' by investigating a gapless parent of the one-dimensional cluster state, obtained by appropriately symmetrizing a commuting projector Hamiltonian for the latter. Projective measurements on the cluster state are known to convert the wavefunction, after post-selection or decoding, into a long-range-ordered Greenberger-Horne-Zeilinger (GHZ) state. Similar measurements applied to the gapless parent (i) generate long-range order coexisting with power-law correlations when post-selecting for uniform outcomes, and (ii) yield power-law correlations distinct from those in the pre-measurement state upon decoding. In the post-selection scenario, rotating the measurement basis preserves long-range order up until a critical tilt angle marking a measurement-induced boundary transition to a power-law-ordered regime. Such a transition establishes new connections between measurement effects on many-body states and non-trivial renormalization-group flows.
12:00 PM Lunch
Lunch
12:00 PM - 2:00 PM
Room: Maskawa Hall
2:00 PM Holographic Network, Parallel Universe and Casimir effect - Rong-Xin Miao (Zhongshan University)
Holographic Network, Parallel Universe and Casimir effect
- Rong-Xin Miao (Zhongshan University)
2:00 PM - 3:00 PM
Room: Maskawa Hall This talk focuses on the gravity dual of CFTs in networks (AdS/NCFT). We prove that the junction condition on the Net-brane leads to conservation laws at network nodes. Additionally, we discuss various proposals for network entropy, confirm that the type I and II network entropies obey the holographic g-theorem, and show that the type III network entropy is non-negative. We show that AdS/NCFT provides a natural way to envision traversable parallel universes that have different geometries and physical laws. Interestingly, unlike traversable wormholes, our model of parallel universes satisfies all the energy conditions. Lastly, if time permits, we will comment on the bounds of the network Casimir effect.
3:00 PM Coffee break
Coffee break
3:00 PM - 3:30 PM
Room: Maskawa Hall
3:30 PM Scale Invariance without Conformal Invariance in Magnetic Systems - Toshiki Onagi (YITP)
Scale Invariance without Conformal Invariance in Magnetic Systems
- Toshiki Onagi (YITP)
3:30 PM - 4:00 PM
Room: Maskawa Hall Wilson introduced the concept of the renormalization group to statistical physics, providing a universal understanding of critical phenomena. According to this framework, it is generally believed that scale invariance at the critical point leads to the emergence of conformal invariance. However, there exist materials in nature, such as the ferromagnet EuS, that exhibit scale symmetry but lack conformal symmetry at criticality. In this talk, I will explain the mechanism behind this peculiar property. Furthermore, I will present non-perturbative results concerning these systems.
4:00 PM Yang-Mills Flux Tube in AdS - Jiaxin Qiao (KITP)
Yang-Mills Flux Tube in AdS
- Jiaxin Qiao (KITP)
4:00 PM - 4:30 PM
Room: Maskawa Hall We initiate the study of flux tubes in confining gauge theories placed in a rigid AdS background, which serves as an infrared regulator. Varying the AdS radius from large to small allows us to interpolate between the flat space confining string, and a weakly coupled string-like object which is held together by the AdS gravitational potential. At any radius, the string preserves a subgroup of AdS isometries equivalent to the one-dimensional conformal group and hence, from the boundary point of view, can be thought of as a conformal defect. The defect hosts a protected operator, called displacement, which nonlinearly realizes the broken AdS isometries. At small radius the displacement corresponds to the gauge field strength inserted at the boundary, while at large radius it is mapped to the Goldstone mode living on the string worldsheet. This relates gauge field and worldsheet degrees of freedom. We propose a hypothesis according to which the large and small radius perturbative expansions can be smoothly matched with each other. As a test, we calculate the leading order corrections to the scaling dimensions and OPE coefficients of a set of defect operators at weak coupling in planar 3D Yang-Mills.
4:30 PM Insights from the crosscap state toward a rigorous formulation of non-orientable TQFTs - Ippo Orii (KITP)
Insights from the crosscap state toward a rigorous formulation of non-orientable TQFTs
- Ippo Orii (KITP)
4:30 PM - 5:00 PM
Room: Maskawa Hall A topological quantum field theory (TQFT) is a class of field theories that have been successfully formulated in a mathematically rigorous way, providing a framework for describing physical phenomena independent of the spacetime metric. In particular, (2+1)-dimensional TQFTs—exemplified by Chern–Simons theory—have been extensively studied in both high-energy and condensed-matter physics as toy models of low-dimensional quantum gravity and as effective theories describing the fractional quantum Hall effect. TQFTs with time-reversal symmetry are equivalent to considering such theories on non-orientable manifolds. However, While these systems exhibit rich mathematical structures, many physical aspects remain unresolved, and a complete mathematical formulation is still lacking. Among the most important objects for analyzing time-reversal-symmetric TQFTs is the crosscap state, which captures the essential features of non-orientable TQFTs. In this talk, I will introduce the axioms of a TQFT, then provide an overview of the current understanding of systems with time-reversal symmetry through the study of crosscap states, incorporating some of my recent results. If time permits, I will also present a new idea suggesting that the study of crosscap states may contain key insights toward a rigorous mathematical formulation of non-orientable TQFTs.