Keio HEP group

TBA
TBA

Wilson-'t Hooft classification and dyonic loops in 3d monopole semiclassics
The phases of gauge theories with Z_N 1-form symmetry are classified by the behavior of line operators, such as Wilson loops and 't Hooft loops. In this talk, we investigate the long-distance behavior of dyonic loop operators in weakly coupled confining phases of 4d SU(N) gauge theories on R^3 x S^1, where confinement is described by a gas of monopole-instantons. We reveal that, in evaluating these loop operators, one must carefully account for emergent symmetries and screening dynamics. Specifically, we demonstrate that properly dressing the 't Hooft loop by a defect known as a twist vortex is essential to derive the correct long-distance behavior consistent with the kinematic predictions of the Wilson-'t Hooft classification. In addition, we discuss the relationship between dyonic loops and the topological nature of the domain walls in the thermal deconfined phase.

Kaluza-Klein photon corrections to charged black hole in two-dimensional perspective
We study the thermodynamics of charged black holes in $D$-dimensional Einstein-Maxwell theory from a two-dimensional perspective. An effective two-dimensional dilaton gravity theory is derived by integrating over the internal $(D-2)$-dimensional sphere as higher-dimensional quantum analyses are technically involved. In particular, the one-loop contributions to the dilaton potential from the massive Kaluza–Klein photons originating from the $U(1)$ gauge field and the metric under the reduction are evaluated explicitly. We find that these modes correct the black-hole charge and entropy, and induce higher-order curvature terms in the effective dilaton potential. Upon neglecting higher-order curvature effects (away from the black hole), the resulting two-dimensional theory reproduces the same semiclassical phase structure, including the Hawking-Page transition, as the original higher-dimensional theory.

Thermodynamics of fermionic excitations in heavy-quark QCD
We investigate the thermodynamic properties of fermionic excitations in heavy-quark QCD on the lattice with Wilson fermions. The grand potential is calculated analytically in the hopping parameter expansion (HPE) on the basis of the cumulant expansion. Using the grand potential, we compute the quark number susceptibilities and their ratios up to next-to-leading order in the HPE. The ratio of fourth- to second-order susceptibilities is shown to be unity (nine) in the deconfined (confined) phase at the leading order. Excitation properties of baryonic and quark modes in each phase are also investigated utilizing the Boltzmann statistics. We obtain an analytic formula for the quark excitation energy in the deconfined phase, while that for baryonic excitations in the confined phase is decomposed into flavor multiplets.

Invitation to Random Tensor Models: from random geometry, enumeration of tensor invariants, to characteristic polynomials
I will introduce random tensor models by first reviewing their motivation coming from random geometric approach to quantum gravity. Then, I will selectively present some of the interesting research results, by highlighting recent results on enumeration of graphs representing tensor invariants, and reporting our recent work on a new notion of characteristic polynomials for tensors via Grassmann integrals and distributions of roots of random tensors. The latter two are based on arXiv:2404.16404 [hep-th] and arXiv:2510.04068 [math-ph]

Classification of color superconductivity revisited
The dense region of the QCD phase diagram, particularly concerning theground state of color superconductor at densities below the onset ofcolor-flavor locking (CFL), remains unsettled to date. This uncertaintystems from various complexities, including the effect of strangequark mass, which splits apart the Fermi surfaces and breaks the pairing.
In this seminar, I revisit the classification of color superconductivity based on the one-gluon exchange helicity amplitude at weak coupling, focusing solely on homogeneous pairing. This framework was initially explored in the seminal work of Bailin and Love but has since been largely overlooked within the community. I will begin the talk by outlining the importance of this somewhat abandoned research field, especially as interest in the dense region of the phase diagram continues to rise and the relevance of colorsuper conductivity becomes increasingly apparent.
I will demonstrate that the loss of Lorentz invariance in the dense medium, together with the decoupling of renormalization group equations, enables us to categorize the possible pairing pattern in color superconductivity ina manner analogous to the nonrelativistic case.
The talk is based on my recent papers, arXiv:2508.19222; 2508.19728

Mathematical studies on Landau-Lifshitz energy: Variational and Dynamical problems
The Landau-Lifshitz energy is a central component of micromagnetics, serving as a powerful and effective tool for the theoretical analysis of magnetization in ferromagnets. Accordingly, the mathematical community has been studying the associated mathematical problems, to establish a rigorous mathematical foundation and to provide support on physical studies. In this talk, I will provide an overview of known mathematical studies on variational and dynamical problems related to Landau-Lifshitz energy. I will also discuss the current scope and future directions of this research field. For nonspecialists, technical aspects will be either simplified or supplemented as much as possible.

Generalized Entropic Cosmology
The thermodynamics of black holes inspired the concept of black hole entropy, linking gravity and thermodynamics. When applied to cosmology, this leads to the standard Friedmann equations, which face challenges in explaining the universe’s evolution. Modified entropies have been proposed to resolve these issues. A recently introduced four-parameter generalized entropy unifies several known forms. Studying this framework offers insights into which entropic models align with observational data. It also allows for consistent cosmological evolution, including inflation, potentially matching Planck results even with scalar field potentials previously ruled out by standard models.

Hopfion approach to glueballs
Glueballs, particles composed of gluons alone, play a key role in addressing one of the most challenging problems in modern physics: color confinement and the origin of mass in QCD. In the dual superconductor picture, glueballs can be viewed as closed flux tubes. It has been conjectured that such states are described by topological solitons with knotted structures, known as Hopfions, in a low-energy effective model of QCD. In this talk, we develop a model of glueballs in terms of Hopfions. We perform semiclassical quantization of Hopfions and assign quantum numbers, such as spin, to these configurations. As a result, we obtain a quantized mass formula for Hopfions. We find that the Hopfion energy spectra are compatible with the prediction of glueball mass by lattice QCD, and that there exist some glueball candidates observed in experiments of which mass agrees very accurately with Hopfion energy.

Thermodynamics of magnetovortical matter from finite-rotation field theory
Rotation is an intriguing external field not only in classical mechanics but also quantum theory. This talk shows recent theoretical developments in the thermodynamics of relativistic rotating systems, extending beyond the Landau-Lifshitz-Pitaevskii framework. In particular, a crucial refinement in gauge theory provides a novel insight into angular momentum under both rotation and magnetic field. This opens up a new direction of studies in quantum many-body systems.

Controlled Diagonal Catalyst Improves the Efficiency of Quantum Annealing
Quantum annealing is a promising algorithm for solving combinatorial optimization problems. According to the adiabatic theorem, the runtime required for quantum annealing to satisfy the adiabaticity scales is inverse to the square of the minimum energy gap between the ground state and the first excited state during time evolution. As a result, finding the ground state becomes significantly more difficult when the energy gap is small, creating a major bottleneck in quantum annealing. Expanding the energy gap is one strategy to improve the performance of quantum annealing, however, its implementation in actual hardware remains challenging. This study proposes a method for efficiently solving instances with small energy gaps by introducing additional local terms to the Hamiltonian and exploiting the diabatic transition remaining in the small energy gap. The proposed method achieves an approximate square speed up in time-to-solution compared to the conventional quantum annealing.

Black Brane Solutions in Heterotic String Theory
Heterotic string theory has non-supersymmetric branes whose existence is suggested by the cobordism conjecture. We numerically construct static, spherically symmetric and asymptotically flat black brane solutions in ten dimensional heterotic string theories for 0- and 4-branes. These branes carry charges that are measured by Chern classes on the sphere surrounding the branes. For the extremal case, the solutions have a throat region with a linear dilaton profile as expected from the corresponding world sheet theory. We also construct non-extremal solutions by compactifying the time direction. To verify the reliability of our numerical calculations, we confirm that they reproduce the known analytical solutions for the 6-brane. Our black brane solutions provide evidence supporting the existence of such branes in heterotic string theory. In this talk, I will explain our motivation for constructing these solutions in heterotic string theory, and then discuss how to realize them.

Exact WKB in all sectors
Exact WKB (EWKB) is one of the most powerful tools to study differential equations and has many applications including quantum mechanics, SUSY gauge theories, QFT with classical backgrounds etc. Being an incorporation of resurgence theory and the traditional WKB method, EWKB method reveals the exact quantization of the physical systems. However, in its standard treatment, the EWKB techniques are restricted to only a single sector which is bounded by singular points on the moduli space. In this talk, I will introduce a novel EWKB approach which displays the continuous connec-tion between different sectors via an analytical continuation preventing singularities. My focus will be on one dimensional potentials with degenerate saddles. With the Airy-type EWKB method, I will show the smooth transition of the spectrum between different sectors. In addition to that with the Weber-type EWKB method, I will present exact estimations to WKB actions in relation with multi-instanton configurations. This reveals the S-duality between minima and maxima of the degenerate potentials in the language of EWKB method. I also show an S-transformation of resurgence relations of genus-1 potentials.