Quantum field theory is a framework that can describe universal behavior in the low-energy region for quantum many-body systems, but solving it is often very difficult as it often becomes strongly coupled systems. One of possible approaches to such problems is to constrain the dynamics from general viewpoints instead of solving the dynamics directly. Symmetry in field theories has played a...
Recently, the concept of symmetry has been generalized, and what was not traditionally called symmetry is now being used similarly as symmetry. In this talk, we discuss a class of such generalized symmetries, called non-invertible symmetries, from the viewpoint of the lattice field theories. In particular, we construct topological defects in four-dimensional Z$_2$ lattice gauge theory,...
It is now understood that the concept of symmetry in quantum field theory should be vastly generalized from the ones come from a group action on fields. The generalization includes the higher-form symmetry, which acts on extended operators, and non-invertible symmetry, which does not have an inverse operation. In particular, a classical symmetry with an ABJ-anomaly with an abelian gauge group...
The IKKT matrix model is a candidate for the non-perturbative formalization of superstring theory in 10 dimension. This model suggests that the (9+1)-dimensional Lorentz symmetry is spontaneously broken and (3+1)-dimensional space-time emerges. However, the sign problem is the main obstacle to the numerical analysis of this model. Recently, numerical studies has been conducted by complex...
Solitonic symmetry is believed to follow the homotopy-group classification of topological solitons. Here, we point out a more sophisticated algebraic structure when solitons of different codimensions coexist in the spectrum. We uncover this phenomenon in a concrete quantum field theory, the $4$d $\mathbb{C}P^1$ model. This model has two kinds of solitonic excitations, vortices and hopfions,...
The IKKT matrix model was conjectured to provide a non-perturbative definition of the type IIB string theory. One of the most attractive features of this model is that spacetime emerges dynamically by interpreting the matrix degrees of freedom as ten-dimensional spacetime coordinates. There have been many numerical simulations suggesting the appearance of (3+1)-dimensional expanding universe....
The Chiral Soliton Lattice (CSL) is a lattice structure composed of domain walls aligned in parallel at equal intervals, which is energetically stable in the presence of a background magnetic field and a finite (baryon) chemical potential due to the topological term originated from the chiral anomaly. We study its formation from the vacuum state, with describing the CSL as a layer of...
Since Gaiotto et.~al discussed the low-energy dynamics of gauge theories on the basis of the mixed ’t Hooft anomaly between discrete and higher-form symmetries, this type of application of the anomaly has been studied vigorously. In this study, in order to understand this type of application of the anomaly in a completely regularized framework, we formulate the fractional topological charge...
In this talk, I will introduce an exact duality in (2 + 1)d between the fermionization of a bosonic theory with a $Z_2$ subsystem symmetry and a fermionic theory with a $Z_2$ subsystem fermion parity symmetry. A typical example is the duality between the fermionization of the plaquette Ising model and the plaquette fermion model. I will establish the exact duality on the lattice by using the...
We consider the phase structure of the linear quiver gauge theory, using the 't Hooft anomaly matching condition. This theory is characterized by the length $K$ of the quiver diagram. When $K$ is even, the symmetry and its anomaly are the same as those of massless QCD. Therefore, one can expect that the spontaneous symmetry breaking similar to the chiral symmetry breaking occurs. On the other...
It is known that the field-theoretic model describing fractons, which have attracted much attention in condensed matter physics, is a theory with non-Lorentz covariant symmetry, called subsystem symmetry. More recently, a fermionic field theory that seems to be related to fractons has been constructed. In this presentation, we discuss detailed properties of these field theories.
Recent studies on the 't Hooft anomaly matching condition for 4D SU($N$) gauge theory have suggested that the phase structure at $\theta=\pi$ should be nontrivial. Namely, some symmetry will be spontaneously broken, or gapless modes will appear. In the large-$N$ limit, it is known that CP symmetry at $\theta=\pi$ is broken in the confined phase, while it restores in the deconfined...
Generalized thimble method is one of powerful methods to overcome the sign problem in numerical simulations. We point out that the method has a subtle property when applied to a nearly continuum system. The point is that solutions of the flow equation generically show exponential behavior, and the growing rates largely differ depending on the modes. It implies the ranges of the flow time...
The Standard Model of particle physics accounts for all experimental observations to date, and may provide viable parameterisation up to the Planck scale. In this eventuality, further insight into the fundamental origin of the Standard Model parameters can only be gleaned by synthesising it with gravity. String theory provides a framework for the construction of phenomenological models that...
The numerical sign problem is one of the major obstacles to first-principles calculations in a variety of important systems. Typical examples include finite-density QCD, some condensed matter systems such as strongly correlated electron systems and frustrated spin systems, and real-time dynamics of quantum fields. Until very recently, individual methods were developed for each target system,...
Recently, a novel approach using tensor renormalization group (TRG) has made great progress in the numerical computation of lattice field theory. In the TRG, partition functions and correlation functions are represented as tensor networks. Their values can be evaluated by coarse-graining the network without using probabilities like Monte Carlo methods. Therefore, the TRG can easily be applied...
I report on recent developments in the generalized thimble method based on the Hybrid Monte Carlo algorithm using backpropagation. In particular, I discuss interesting results for the IKKT matrix model and the real-time evolution in quantum mechanics.
We propose a lattice fermion formulation with a curved domain-wall mass term as a nonperturbative regularization of quantum field theory in a gravitational background. In KEK-TH 2021 last year, we reported that the edge-localized modes appear on the curved domain-wall in free fermion theory on a square lattice, and they feel gravity through the induced spin and spin-c connections. We...
Inside topological insulators or in the theta=pi vacuum, magnetic monopoles gain fractional electric charges, which is known as the Witten effect. In this work, we try to give a microscopic description for this phenomenon, solving a "negatively" massive Dirac equation. The "Wilson term" plays a key role in 1) identifying the sign of the fermion mass, 2) confirming evidence for dynamical...
Recently, the tensor network description with bond weights on its edges has been proposed as a novel improvement for the tensor renormalization group (TRG). The bond weight is controlled by a single hyperparameter, whose optimal value is estimated in the original work via the numerical computation of the two-dimensional critical Ising model. We develop this bond-weighted TRG algorithm to make...
We study the time dependent behavior of a quantum pendulum by path-integral and Wigner-Weyl phase space quantum mechanics. In both cases, we encounter a negative sign problem, and propose certain approximation similar to the truncated Wigner approximation, which sheds some light on the sign problem.
We study the periodic complex action theory (CAT) by imposing a periodic condition in the future-included CAT where the time integration is performed from the past to the future, and extend a normalized matrix element of an operator O, which is called the weak value in the real action theory, to another expression. We present two theorems stating that the expression becomes real for O being...
The range of motion of a particle with certain energy $E$ confined in a potential is determined from the energy conservation law in classical mechanics. The counterpart of this question in quantum mechanics can be thought of as what the possible range of the expectation values of the position operator $⟨x⟩$ of a particle, which satisfies $E=⟨H⟩$. This range would change depending on the state...
The linear differential system of the $\mathcal{N}=1$ super affine Toda field equations (ATFEs) (Classical) with Lie superalgebras is studied. The modified linear equations reduce to a couple of ordinary differential equations (ODEs). The $osp(2|2)^{(2)}$ giving the Schrodinger equation with squared potential verifies the ODE/IM correspondence.
Quantum tunneling has been playing an important role in various fields of theoretical physics. So far, the only way for us to gain insights into the mechanism is to use the instanton method, which is based on imaginary-time formalism. However, to study its dynamics, it is essential to use real-time formalism, whose path integral is highly oscillatory. Fortunately, Picard-Lefschetz theory can...
The MERA has attracted attention as a model that describes the geometry that emerges from boundary theory. Its continuous version, the cMERA, is expected to be a method to derive geometry directly from a continuous theory. In free field theories, the cMERA was successfully constructed based on the variational method. However, from the holographic point of view, it is crucial to construct the...
We find the exact solutions of the $\Phi_{2}^{3}$ finite matrix model (Grosse-Wulkenhaar model). In the $\Phi_{2}^{3}$ finite matrix model, multipoint correlation functions are expressed as $G_{|a_{1}^{1}\ldots a_{N_{1}}^{1}|\ldots|a_{1}^{B}\ldots a_{N_{B}}^{B}|}$. The $\sum_{i=1}^{B}N_{i}$-point function denoted by $G_{|a_{1}^{1}\ldots a_{N_{1}}^{1}|\ldots|a_{1}^{B}\ldots a_{N_{B}}^{B}|}$ is...
We propose a fluid model of self-gravitating strings. It is expected that black holes turn into strings around the end of black hole evaporation. The transition will occur near the Hagedorn temperature. After the transition, strings would form a bound state by the self-gravitation. Horowitz and Polchinski formulated a model of self-gravitating strings by using winding strings wrapping on the...
Krylov complexity is a measure of operator growth that is considered to capture quantum chaos in lattice systems. We study the Krylov complexity and Lanczos coefficients of free scalar theories and their perturbative theories in the continuum limit. In particular, we discuss the effects of mass, hard UV cutoff, thermal mass, and perturbative interactions.
The D-term is one of the conserved charges of hadrons defined as the forward limit of the gravitational form factor D(t). We calculate the nucleon’s D-term in a holographic QCD model in which the nucleon is described as a soliton in five dimensions. We show that the form factor D(t) is saturated by the exchanges of infinitely many 0++ and 2++ glueballs dual to transverse-traceless metric...
We consider type IIB orientifold models in four-dimensional Minkowski spacetime, with N=2 supersymmetry spontaneously broken to 0. For an arbitrary choice of D9- and D5-brane configuration, we analyze the generation of masses at one-loop for all open- and closed-string sector moduli fields. In order to find non-tachyonic models at one-loop, a key ingredient is to consider brane configurations...
In order to avoid contradictions with complementarity and causality in a gedankenexperiment involving a quantum superposition of a massive body, it was previously shown (in arXiv:1807.07015) that it is necessary for there to be both quantized gravitational radiation and local vacuum fluctuations
of the spacetime metric. We review this gedankenexperiment and the previously given “back of the...
Expanding edge experiments are promising to open new physics windows of quantum Hall systems. In a static edge, the edge excitation, which is described by free fields decoupled with the bulk dynamics, is gapless, and the dynamics preserve conformal symmetry. When the edge expands, such properties need not be preserved. We formulate a quantum field theory in 1+1 dimensional curved spacetimes to...
In this talk, I discuss how one can systematically construct non-supersymmetric string vacua with vanishing cosmological constant at one loop, founded mainly on a series of my works. After making a review of related studies, I present the constructions of the string vacua possessing such a property based on the asymmetric orbifolds in various CFT set-ups. We further discuss the physical...
We investigate properties of the conserved charge in general relativity, recently proposed by one of the present authors with his collaborators, in the inflation era, the matter dominated era and the radiation dominated era of the expanding Universe. We show that the conserved charge becomes the Bekenstein-Hawking entropy in the inflation era, and it becomes the matter entropy and the...
It is known that the partition function of ABJM theory, the 3d Chern-Simons matter theory on N M2-branes probing $C^4/Z_k$ orbifold, solves a non-linear difference relation called q-deformed Painleve III system. This connection is motivated with the idea of Painleve/gauge correspondence and the topological string/spectral theory correspondence for the quantization of algebraic curves, which...
We propose a systematic way of obtaining 6d Seiberg-Witten curves from Type IIB 5-brane webs with or without orientifold planes, by generalizing the construction of 5d Seiberg-Witten curves from 5-brane webs. We apply our construction to two kinds of theories: 6d E-string theory and little string theory. In particular, the expression of Seiberg-Witten curve for the E-string theory...
In effective field theory, the positivity bounds of higher derivative operators are derived from analyticity, causality, and unitarity. We show that the positivity bounds on a class of effective field theories, e.g., dimension-eight term of a single massless scalar field, the Standard Model Effective Field Theory dimension-eight $SU(N)$ gauge bosonic operators, and Einstein-Maxwell theory with...
We axiomatize rational massless renormalization group flow as Kan extension.
In minisuperspace quantum cosmology, the Lorentzian path integral formulations of the no-boundary and tunneling proposals have recently been analyzed, but it has been pointed out that the wave function of linearized perturbations around a homogeneous and isotropic background is of an inverse Gaussian form and thus that their correlation functions are divergent. In this talk, I will discuss the...
In 1973, Yoichiro Nambu published a GHD paper(titled Generalized Hamitonian Dynamics). This paper was the beginning of what is now known as Nambu dynamics. Nambu dynamics is the generalization of Hamiltonian dynamics involving multiple Hamiltonians, and has applications to string theory and fluid dynamics. In this talk, We will present our successful formulation of Nambu dynamics...
Quantum cosmology is established as a way to understand the beginning of universe. Picard-Lefschetz theory has raised recent interest on the “tunneling from nothing” proposal by Vilenkin and the “no boundary” proposal by Hartle-Hawking. The two proposals can be closely related through analysis on saddle points and boundary conditions. In this work, we demonstrate a first principle calculation...
We study the impacts of matter field Kaehler metric on physical Yukawa couplings in string compactifications. Since the Kaehler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings...
One perturbative string theory is defined on one fixed background. On the other hand, it is necessary that a non-perturbative formulation of string theory includes all the perturbatively stable vacua and perturbative string theories on various curved backgrounds are derived from the single theory. In this talk, we derive perturbative string theories on all the curved backgrounds from the...
