I give a review (, possibly biased, ) on chiral theory as edge modes from a personal point of view. After reviewing the problem of chiral theory on the lattice, I comment on the standard method by symmetric mass generation of mirror fermion.I also review the recent work on chiral boson theory in 1+1 d by M. DeMarco, E. Lake, X.-G. Wen.

Since the establishment of the Standard Model of elementary particles, the research in quantum field theory has investigated non-perturbative analysis based on theories with high symmetry, such as supersymmetry. However, the Standard Model, including QCD, has relatively low symmetry, and it is getting important to analyze theories based on features appearing only in QFT with low symmetry. In...

Quantum cosmology investigates the origins of our Universe, including the concept of "tunneling from nothing" proposed by Vilenkin and Hartle-Hawking. Recent advancements have renewed interest in this field, employing the Picard-Lefschetz theory in Lorentzian quantum gravity. In this study, we address crucial challenges using the generalized Lefschetz thimble method, overcoming the sign...

Photon spheres are the characteristic of general black holes, thus are a suitable touchstone for the emergence of gravitational spacetime in the AdS/CFT correspondence. We provide a spectral analysis of an AdS Schwarzschild black hole near its photon sphere. We find that quasinormal modes near the photon sphere reflect the AdS boundary, resulting in a peculiar spectral pattern. Our large...

Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic system, and numerically evaluate Krylov complexity for operators and states. Despite no exponential growth of the Krylov complexity, we find a clear correlation...

The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. Recently, we have performed complex Langevin simulations adding a Lorentz invariant mass term as an IR regulator. In this talk, we will show that the (3+1)-dimensional expanding space-time emerges due to the effect of fermions.

The local gauge symmetry remaining even after imposing a gauge fixing condition is called the residual local gauge symmetry, which is spontaneously broken in the perturbative vacuum, and is expected to be restored in the true confining vacuum. Indeed, the criterion for restoring a special choice of the residual gauge symmetry was shown to be equivalent to the Kugo-Ojima color confinement...

We apply the gradient flow exact renormalisation group (GFERG) for scalar quantum electrodynamics. The flow equations for the Wilsonian effective action is derived by means of perturbative expansion in the gauge coupling. In this work, we deal with quantum corrections to the correlation functions up to second order of the gauge coupling. We demonstrate especially that the GFERG formalism...

Under the Hamiltonian evolution, a simple operator turns into a complicated operator. The growth of such an operator is drastically different when the system is connected to a dissipative environment than in a typical closed system. We probe such growth via a recently explored measure of scrambling known as Krylov complexity and aim to propose an operator growth hypothesis in open quantum...

Bifundamental QCD, an $SU(N) \times SU(N)$ gauge theory with a bifundamental fermion, has received substantial attention due to its rich phase structure and its notable relevance to the large-$N$ orbifold equivalence. To investigate the vacuum structure and phase diagrams of this model, we employ a semiclassical center-vortex description of the confining vacuum, enabled through...

Motivated by the picture of partial deconfinement developed in recent years for large-N gauge theories, we propose a new way of analyzing and understanding thermal phase transition in QCD. We find nontrivial support for our proposal by analyzing the lattice configuration for 4d SU(3) QCD with dynamical quarks, produced by WHOT-QCD collaboration. In the discussion, the Polyakov line plays a...

We find new bilinear relations for the partition functions of $U (N)_k × U(N+M)_{−k}$ ABJ theory with two parameter mass deformation (m1,m2), which generalize the q-Toda-like equation found previously for m1=m2. By combining the bilinear relations with the Seiberg-like dualities and the duality cascade relations, we can determine the closed form expressions of the partition functions...

We talk about Page curves for 2d black holes with multiple injections. The feature is that a decreasing entanglement entropy related to time is replaced with a increasing one when a energy is injected. After each energy injection, we find a sudden increase in the entropy, and also subsequent increasing period. Then, after a "Page time", there comes a decreasing period untill the next energy...

We propose three distinct methods to compute the mass of composite particles (hadrons) of gauge theories in the Hamiltonian formalism. Determination of the mass spectrum of hadrons is one of the key issues in QCD, which has been precisely calculated by the Monte Carlo simulation based on the Lagrangian formalism. We newly show how to compute the mass spectra in the Hamiltonian formalism, which...

In perturbative string theory, there have mainly been two ways to quantize the string. Either one quantizes in lightcone gauge, or one quantizes covariantly. The difference between them is only gauge condition, and the equivalence of on-shell amplitudes had been already shown. String field theory is a candidate for a non-perturbative formulation of string theory. There have mainly been two...

The IKKT matrix model was proposed in 1996 as a non-perturbative description of superstring theory. One of its appealing features is the fact that spacetime emerges naturally from first principles as the eigenvalue distribution of the bosonic matrix degrees of freedom. For the past few decades, there has been extensive number of numerical attempts to study the model. In this work, we...

The IKKT matrix model is the most promising candidate of a non-perturbative formulation of superstring theory. Recently it has been proposed to introduce the Lorentz invariant mass term as a regularization. This model has SO(9,1) Lorentz symmetry, and a partition function diverges due to the non-compactness of the volume of the Lorentz group. In this study, we have done the analytical...

The giant graviton expansion of the superconformal index gives the finite rank corrections to the calculation of the index of the superconformal field theory via AdS/CFT correspondence. We study the giant graviton expansions focusing on the 4-dimensional N=2 superconformal field theories realized on D3-branes in 7-brane backgrounds with constant axiodilaton. For some theories including them,...

The type IIB matrix model is a promising candidate for a nonperturbative definition of superstring theory. The Lorentzian version, however, is not well defined as it is, and it was recently proposed to introduce a Lorentz invariant mass term in the action as an IR regulator. Depending on the sign of this term, we either have a model that is truly Lorentzian or one that is comparable to the...

We examine symmetries of chiral four-dimensional vacua of Type IIB flux compactifications with vanishing superpotential W=0. We find that the N=1 supersymmetric MSSM-like and Pati-Salam vacua possess enhanced discrete symmetries in the effective action below the mass scale of stabilized complex structure moduli and dilaton. Furthermore, a generation number of quarks/leptons is small on these...

In this talk, we revisit the "derivation" of the IKKT matrix model from perturbative string theory and discuss how we should define the path integral of the matrix model. In course of the "derivation," we will see that kappa symmetry is formally enhanced and that there is a subalgebra of the gauge symmetry closed off-shell, in sharp contrast to the fact that the kappa symmetry in the...

We consider a 4D spherically-symmetric static spacetime region as a collection of quanta in the semi-classical Einstein equation and study the entropy including the self-gravity. For sufficiently excited states, we estimate the entropy in a WKB-like method considering the non-locality of entropy and local consistency with thermodynamics and find its upper bound. The saturation condition...

One of the goals in quantum field theory is to identify long distance behaviors of a theory defined at a short distance. One criterion to distinguish long distance behaviors is the precense of gap. When it is gapped, in two-dimensional space(time), the phases stand in bijection with module categories. In particular, ground state degeneracies (GSDs) of gapped phases are given by ranks of module...

Homotopy algebras algebras have been contributed to describe string field theory effectively. Recently, it has been recognized that these algebras can also be used to express quantum field theory, and its formulas are believed to be universal. In the recent research, it is presented that correlation functions of scalar field theories can be written in terms of homotopy algebras. In this talk,...

In this talk, I demonstrate that scale invariance and electromagnetic duality are strong enough to restrict the spacetime dimension. 10 and 11 dimensional spacetimes are obtained as solutions of these constraints. In this derivation, supersymmetry and general relativity are not assumed.

In this talk, we will discuss possible holographic dual of de Sitter Space from two different ideas. One is the original dS/CFT correspondence, and we will present an explicit CFT dual for three dimensional de Sitter space and examine its properties. The other is to study a holographic dual of a half de Sitter space, which has a time- like boundary. After we explain the results based on these...

We study the properties of the Petz recovery map in chaotic systems, such as the Hayden-Preskill setup for evaporating black holes and the SYK model. Since these systems exhibit the phenomenon called scrambling, we expect that the expression of the recovery channel $\mathcal{R}$ gets simplified, given by just the adjoint $\mathcal{N}^{\dagger}$ of the original channel $\mathcal{N}$ which...

We extend the definition of Lüscher's lattice topological charge to the case of 4d SU(N) gauge fields coupled with Z_N 2-form gauge fields. This result is achieved while maintaining the locality, the SU(N) gauge invariance, and Z_N 1-form gauge invariance, and we find that the manifest 1-form gauge invariance plays the central role in our construction. This result gives the lattice regularized...

We study non-invertible duality symmetries by gauging a diagonal subgroup of a non-anomalous U(1) × U(1) global symmetry. In particular, we employ the half-space gauging to c=2 bosonic torus conformal field theory (CFT) in two dimensions and pure U(1) × U(1) gauge theory in four dimensions. In c=2 bosonic torus CFT, we show that the non-invertible symmetry obtained from the diagonal gauging...

We present the lattice simulation of the renormalization group flow in the 3-dimensional O(N) linear sigma model. This model possesses a nontrivial infrared fixed point, called Wilson-Fisher fixed point. Arguing that the parameter space of running coupling constants can be spanned by expectation values of operators evolved by the gradient flow, we exemplify a scaling behavior analysis based on...

We consider non-invertible symmetries in Maxwell theories on a non-spin manifolds. Since line operators can be either bosonic or fermionic on such manifolds, three slightly different Maxwell theories without an anomaly can be formulated. We investigate the behaviors of these theories under gauging one-form symmetries, and construct non-invertible symmetries on these theories from half gauging.

We demonstrate a universal mechanism of a class of instabilities in infrared regions for massless Abelian p-form gauge theories with topological interactions, which we call generalized chiral instabilities. Such instabilities occur in the presence of initial electric fields for the p-form gauge fields. We show that the dynamically generated magnetic fields tend to decrease the initial electric...

The admissibility conditions are essential for obtaining a well-defined topological charge in lattice gauge theory. However, these conditions may naively seem to prohibit the existence of magnetic operators, as they automatically enforce the Bianchi identity. In this presentation, we will explain how this issue is addressed in the context of 2-dimensional compact scalar theories on a lattice....

We summarize our recent attempt to construct a bulk spacetime from a scalar CFT such as an O(N) vector model by a conformal flow, which generates bulk fields from boundary scalar fields by smearing them. In this approach, bulk correlation functions are completely determined by the boundary theory, while bulk geometry is unspecified. We propose a method to determine the bulk geometry depending...

The Witten effect predicts that a magnetic monopole acquires a fractional electric charge inside topological insulators. In this work, we give a microscopic description of this phenomenon as well as an analogous two-dimensional system with a vortex. We solve the Dirac equation of electron field both analytically in a continuum and numerically on a lattice by adding the Wilson term and smearing...

We discuss the phase structure of the fundamental Kazakov-Migdal (FKM) model, which is defined on graphs and a generalization of the Kazakov-Migdal model by replacing the scalar fields in the adjoint representation with the fundamental representation. We first show that the partition function of the FKM model can be represented by the unitary matrix valued graph zeta functions, which...

String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this theory, strings constitute not only particles but also the space-time. In this talk, in string geometry theory, we identify perturbative vacua in string theory, which include general string backgrounds. From fluctuations around these vacua, we derive the path-integrals of perturbative...

It has been suggested that quantum error correction plays a significant role in the AdS/CFT correspondence. It has also been pointed out that a tensor network given by MERA can be viewed as bulk space emerging from a boundary theory through the structure of the renormalization group. Motivated by these insights, we demonstrate that the renormalization group serves as an approximate quantum...

We propose a mathematical formulation of the Atiyah-Singer index on a lattice. Employing a one-parameter family of the massive Wilson Dirac operator, our lattice definition of the index does not rely on chiral symmetry or Ginsparg-Wilson relation. We give a mathematical proof that at fine but finite lattice spacing, our definition converges to the index in the continuum theory. This talk is...

In this talk, we discuss the black hole/string transition in the black hole evaporation. Susskind proposed that a black hole turns into a highly excited string as one adiabatically decreases the string coupling. Horowitz and Polchinski constructed a model of string bound state which describes the string phase of the black hole/string transition. In the previous work, we extended the...

Dealing with multiple flavors of Wilson fermions with Grassmann TRG is known to be difficult due to the exponential growth of the tensor size. Here, we propose a way to overcome this problem by separating the initial tensor into layers, each corresponding to different flavor. A compression scheme for the initial tensor is also proposed to further reduce the size. We test our method by studying...

The tensor renormalization group (TRG) method was originally proposed in condensed matter physics and has recently been drawing attention in particle physics. We investigated the shape dependence of entanglement entropy in the two-dimensional Ising model using the TRG method and obtained the central charge of the theory from the scaling property of entanglement entropy. We also developed a...

We revisit the connection between Hawking radiation and high-frequency dispersions for a Schwarzschild black hole following the work of Brout et al.. After confirming the robustness of Hawking radiation for monotonic dispersion relations, we consider non-monotonic dispersion relations that deviate from the standard relation only in the trans-Planckian domain. Contrary to the common belief that...

In this talk, I will discuss the application of the exact WKB analysis to a couple of one-dimensional Schrödinger-type equations reduced from the Stark effect of hydrogen. By introducing Langer’s modification, we prove the exactness of the Bohr-Sommerfeld quantization conditions for the Borel-resummed quantum WKB periods at the weak electric field intensities and also find these quantization...

Holographic complexity is conjectured to probe the evolution of spacetime. For black holes in anti-de Sitter (AdS) spacetime the growth rate of complexity approaches a constant value at late times, while in de Sitter (dS) spacetime it diverges at a finite critical time. In this talk, we consider geometries interpolating between AdS and dS. In particular, we discuss the evolution of volume...

Sequestering is a promising mechanism in 4D string models to reconcile high scale inflation with low-energy supersymmetry. In this scenario the MSSM lives on branes at singularities and it is sequestered from the sources of supersymmetry breaking in the bulk. The soft-terms are suppressed with respect to the gravitino mass so that all moduli are heavy enough to avoid any cosmological moduli...

We previously proposed a mechanism to effectively obtain, after a long time development, a Hamiltonian being Hermitian with regard to a modified inner product $I_Q$ that makes a given non-normal Hamiltonian normal by using an appropriately chosen Hermitian operator $Q$. We studied it for pure states. In this talk we show that a similar mechanism also works for mixed states by introducing...

Wilson's exact renormalization group (ERG) is a fundamental idea for defining quantum field theory at a non-perturbative level. The conventional ERG based on the momentum cutoff, however, cannot preserve the manifest gauge invariance and this fact hinders non-perturbative analyses of gauge theories using ERG. In this talk, I explain the gradient flow exact renormalization group (GFERG), which...

Current problems in quantum gravity and string theory will be summarized and how they may be overcome in the future will be discussed.