I will review a basic notion of higher form symmetries, which are symmetries for extended objects such as vortices, and domain walls. As an application, we discuss spontaneous symmetry breaking of higher form symmetries, topological order, and symmetry-protected topological phases of matter.

It is discussed that the symmetry protected topological phase (SPT phase) is well described by generalized cohomology theory. Identifying the classification of SPT phases on a real-space manifold $X$ as a homology group on $X$ offers a unified understanding of SPT phenomena through the axioms and general properties of the generalized (co)homology. In this talk, I will give a brief review of...

Superconductive gaps have topologically protected nodes if the fermions form the inter-chiral Cooper pair [1]. We generalize this Li and Haldane's argument to the color superconductivity in QCD with one flavor. Among several order parameters with different spins and colors, we find that the nodes in the phases with a simple color-spin structure have the vortices characterized by the Berry...

We study the ground states of low-density hadronic matter and high-density color-flavor locked color superconducting phase in three-flavor QCD at finite baryon chemical potential under rotation. We find that, in both cases under sufficiently fast rotation, the combination of the rotation-induced topological term for the η' meson and the QCD anomaly leads to an inhomogeneous condensate of the...

Gauge anomaly in 4-dimensions can be viewed as a current inflow into an extra-dimension, where the total phase of the fermion partition function is given in a gauge invariant way by the Atiyah-Patodi-Singer(APS) eta-invariant of a 5-dimensional Dirac operator. However, this formalism requires a non-local boundary condition, which makes the physical roles of edge/bulk modes unclear and the...

I will describe how symmetry structures appearing in quantum many-body systems can be understood within the framework of fusion categories. Quantum systems with ``higher symmetry" structures naturally appear by generalising or weakening certain axioms of these fusion categories. I will touch upon various topological aspects of higher group symmetries such as symmetry protected topological...

Dense QCD matter appears in compact astrophysical phenomena and heavy-ion collisions. Phenomenological EOS (equation of state) needs extrapolation or interpolation and has large uncertainty. Thus we need first-principles or model-independent theoretical studies, or experiments where dense QCD matter is directly probed. In this talk, I first review physics of finite density QCD from the...

In this talk, I will explain the recent progress of understanding the QCD phase diagram based on the holographic models. Particularly, this talk concentrates on the treatment of the color superconductivity and the application of the imaginary chemical potential in the bottom-up approach. In addition, I will explain what interesting phenomena will be discussed via the bottom-up holographic models.

Exploring the QCD phase diagram is known to be extremely difficult at finite density due to the sign problem, which occurs in lattice QCD calculations. We show that this problem can be overcome by the complex Langevin method in a certain parameter region at low temperature and high density. This, in particular, gives us a hope to investigate color superconductivity in lattice QCD by first...

In this talk, I will study the quantum entanglement in the momentum space for scalar field theory on a fuzzy sphere. In an interacting quantum field theory, the degrees of freedom in momentum space show entanglement; it quantifies the correlation between the high/low momentum modes. On a fuzzy sphere, an example of noncommutative space, it is known that the UV and IR degrees of freedom show a...

We propose a new vertex formalism, called anti-refined topological vertex (anti-vertex for short), to compute the generalized topological string amplitude, which gives rise to the supergroup gauge theory partition function. We show the one-to-many correspondence between the gauge theory and the Calabi--Yau geometry, which is peculiar to the supergroup theory, and the relation between the...

We study the D-branes on the magnetized extra dimensions and corrections of the flux to the effective theories. Specifically we focus on toroidal compactifications of non-abelian DBI action, and compute the flux corrections to the gauge couplings, the Kaehler metrics of charged matters and the scalar four-point couplings. In this talk, we would like to show the results of the dimensional...

We investigate the bubble nucleation in five dimensional spacetime catalyzed by quintessence. We especially focus on decay of a metastable Minkowski vacuum to an anti-de Sitter vacuum and study dynamics of the bubble on which four dimensional expanding universe is realized. We also discuss the trans-Planckian censorship conjecture and impose a constraint on the parameter space of the...

In six-dimensional F-theory/Heterotic string theory, half-hypermultiplets arise only when they correspond to particular quaternionic Kähler symmetric spaces, which are mostly associated with the Freudenthal-Tits magic square. Motivated by the intriguing singularity structure previously found in such F-theory models with a gauge group SU(6), SO(12) or E_7, we investigate, as the final magical...

We analyze the chiral phase transition of the NambuーJona-Lasinio model in the cold and dense region on the lattice developing the Grassmann version of the anisotropic tensor renormalization group algorithm. The model is formulated with the KogutーSusskind fermion action. We use the chiral condensate as an order parameter to investigate the restoration of the chiral symmetry. The first-order...

We investigate an irrelevant deformation of 2D quantum field theories, called "TT-bar deformation". Although this is known as an integrable deformation, its quantum aspects have not been completely understood yet. For example, TT-bar deformation of the free massless O(N) vector model is said to be Nambu-Goto action in the static gauge. In this talk, we compute the thermal free energies in both...

We study wavefunctions of heavy scalars on de Sitter spacetime and their implications to dS/CFT correspondence. In contrast to light fields in the complementary series, heavy fields in the principal series oscillate outside the cosmological horizon. As a consequence, the quadratic term in the wavefunction does not follow a simple scaling and so it is hard to identify it with a conformal...

Gauge theory with a theta term has recently been of great interest, especially at $\theta=\pi$, where nontrivial phase structure is expected from the 't Hooft anomaly matching condition. However, it is difficult to study the theory numerically due to the severe sign problem. We try to overcome this by using the complex Langevin method. In our previous work, we apply the technique to the 2d...

We establish a correspondence between a class of Wilson-'t Hooft lines in four-dimensional N=2 supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-'t Hooft lines in a twisted product space S^1xR^3 by supersymmetric...

Partial deconfinement is proposed in the context of the deconfinement transition for the large N gauge theories, as the coexisting phenomenon of the confined and deconfined sectors in the space of color degrees of freedom. It is well-established analytically for weakly-coupled theories, while it remains unclear whether the above picture is valid at strong coupling. We provide some evidence for...

The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. In the previous work, Monte Carlo calculations provided interesting results indicating the spontaneous breaking of SO(9) to SO(3) and the emergence of (3+1)-dimensional space-time. There, an approximation was used to avoid the sign problem, however. In this talk, we report...

We study the superconformal index of the 6d (2,0) theory by using the AdS/CFT correspondence. It is well known that on the gravity side at the large N limit, the index can be calculated from the contribution of the Kaluza Klein modes. For the AdS_5/CFT_4 cases, recent works show that in addition to Kaluza Klein modes, D3-branes wrapped on the compact space contribute to the index at the finite...

We briefly overview how historically string theory led theoretical physics first to algebraic/differential geometry, and then to computational geometry, and now to data science.

Using the Calabi-Yau landscape - accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades - as a starting-point and concrete playground, we then launch to review...

We are faced with an explosion of data in many areas of physics, but very so often, it is not the size but the complexity of the data that makes extracting physics from big datasets challenging. As I will discuss in this talk, data has shape and the shape of data encodes the underlying physics. Persistent homology is a tool in computational topology developed for quantifying the shape of data....

Motivated by the recent connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators (OTOCs), we study the pole structure of thermal two-point functions in d-dimensional conformal field theories (CFTs) in hyperbolic space. We derive the pole-skipping points of two-point functions of scalar and vector fields by three methods (one field theoretic...

We discover a new tricritical point realized only in nonequilibrium steady states, using the AdS/CFT correspondence. Our system is a (3+1)-dimensional strongly coupled large-Nc gauge theory. The tricritical point is associated with a chiral symmetry breaking under the presence of an electric current and a magnetic field. The critical exponents agree with those of the Landau theory of...

We argue a smallness of gauge couplings in abelian quiver gauge theories, taking the anomaly cancellation condition into account. In theories of our interest there exist chiral fermions leading to chiral gauge anomalies, and an anomaly-free gauge coupling tends to be small, and hence can give a non trivial condition of the weak gravity conjecture. As concrete examples, we consider U(1)^{k}...

We investigate the history of dark energy to explain the present magnitude. We assume the dark energy is the residual cosmological constant. The most important channel in the reheating process is the gluon pair productions by QCD trace anomaly. We argue dark energy decays rapidly by gluon pair emissions during the reheating and after the big bang. The reheating temperature is determined by the...

We study a classical theory which contains a Gaussian noise as a source. This source is responsible for the creation and annihilation of particle from the vacuum and the energy of the resultant configuration is same as the zero point energy of quantum field theory. We show that after taking the average over the samples, the perturbative expansion of the expectation value, n-point function, can...

Measurements made recently by the STAR collaboration show that the Lambda hyperons produced in relativistic heavy-ion collisions are subject to global spin polarization with respect to an axis coincident with the axis of rotation of the produced matter. Recently formulated formalism of relativistic hydrodynamics with spin, which is a generalization of the standard hydrodynamics, is a natural...

In this talk, I introduce two different approaches to treat the XXZ Heisenberg chain with twisted boundary conditions. One is the linear response theory, which treats the twists as a perturbation. The other is the twisted boson theory, which treats irrelevant terms as a perturbation after considering the effects of the twists. Surprisingly, these two formalisms cannot make the same results. We...

We review the origin and basics of the black-hole information loss paradox, and comment on some of its potential resolutions.

In quantum theory, black holes evaporate. We adopt this property as the 0th approximation and provide a field-theoretic description of black holes. To do that, we analyze time evolution of a spherical collapsing matter together with the back reaction of (pre)Hawking radiation by solving the semi-classical Einstein eq coupled with N massless scalar quantum fields. We find a 4D self-consistent...

We use the replica method to compute the entanglement entropy of a universe without gravity entangled in a thermofield-double-like state with a disjoint gravitating universe. Including wormholes between replicas of the latter gives an entropy functional which includes an "island" on the gravitating universe. We solve the back-reaction equations when the cosmological constant is negative to...

Microstate geometries are smooth horizonless geometries that have the same mass and charge as a black hole. In this talk, I will review the current status of the research in microstate geometries, such as their construction, counting and lifting, and discuss their physical implications, such as evolution toward more typical microstates.

We study the Page curve for asymptotically flat eternal Schwarzschild black holes in four (or higher) spacetime dimensions. Before the Page time, the entanglement entropy grows linearly in time. After the Page time, the entanglement entropy of a given region outside the black hole is largely modified by the emergence of an island, which extends to the outer vicinity of the event horizon. As a...

We construct black hole geometries in 3d AdS with non-trivial values of KdV charges. The black holes are saddle points of the free energy that is holographically dual to that of the generalized Gibbs ensemble containing the chemical potentials of quantum KdV charges in 2d CFT. The introduction of the chemical potentials means the deformation of the boundary Hamiltonian which results in the...