arXiv subjects

Naoto Kan

Publications and source records attributed to Naoto Kan.

At least 19 recordsLinked to original sources

arXiv2026

7-branes and $\Gamma_0(2)$ Duality in Type 0B String Theory

We investigate 7-branes in type 0B string theory, motivated by the recent proposal of Baykara, Dudas, and Vafa, which connects type 0B string theory with M-theory. On the $Q$-symmetric branch, the self-duality group of type 0B string theory is $\Gamma_0(2)$, whose Abelianization is $\mathbb{Z}\times\mathbb{Z}_4$. This implies the existence of two independent 7-brane charges. We construct explicit charge operators in terms of modular forms and identify the corresponding charged objects in gravity solutions. One is the ordinary D7-brane, while the other is a 7-brane carrying a nontrivial $\mathbb{Z}_4$ charge. We further construct a compact background consisting of eight such $\mathbb{Z}_4$ 7-branes using a restricted Weierstrass model. Remarkably, in this background the axio-dilaton is fixed to the constant value $\tau=(1+\mathsf{i})/2$, which coincides with the unstable de Sitter critical point proposed in the M-theory description of type 0B string theory. We also analyze fluctuations in the $Q$-odd sector and find that, although the corresponding equations of motion are globally well-defined in this background, the closed string tachyon remains unstable. Our results provide a concrete realization of new 7-branes in type 0B string theory and clarify their relation to its strong-coupling structure.

hep-th↗

arXiv2025

Emergent higher-form symmetry from type IIB superstring theory

We investigate a higher-form symmetry in type IIB superstring theory, which possesses an ${\rm SL}(2,\mathbb{Z})$ symmetry. From the point of view of the low-energy effective field theory, the ${\rm SL}(2,\mathbb{Z})$ symmetry is treated as a gauge symmetry. Hence, an $8$-form global symmetry $\mathbb{Z}_{12}^{[8]}$ emerges as a quantum symmetry. In this paper, we present an explicit construction of the topological operator associated with the $\mathbb{Z}_{12}^{[8]}$ symmetry. In this construction, the discriminant $\Delta(\tau)$ plays a central role. As a result, it becomes manifest that $\mathbb{Z}_{12}^{[8]}$ is the solitonic symmetry of $7$-branes. Furthermore, taking into account the extensions of the duality group, we also discuss what global symmetries emerge when considering not ${\rm SL}(2,\mathbb{Z})$ but ${\rm Mp}(2,\mathbb{Z})$, ${\rm GL}(2,\mathbb{Z})$, and ${\rm Pin}^+({\rm GL}(2,\mathbb{Z}))={\rm GL}^+(2,\mathbb{Z})$.

hep-th↗

arXiv2025

Time-reversal invariant vortex in topological superconductors and gravitational $\mathbb{Z}_2$ topology

We study a time-reversal invariant vortex, namely a spin vortex, in helical superconductors by focusing on its emergent gravitational structure. The topology of the time-reversal invariant vortex is classified by a $\mathbb{Z}_2$ invariant: helical Majorana zero modes appear at the vortex core when the winding number is odd, while no such zero modes exist when it is even. We provide a formal mapping to the theory of gravity to describe this $\mathbb{Z}_2$ topological structure. Identifying a superconducting order parameter as a vielbein in the theory of gravity, we explicitly convert the Bogoliubov-de-Genne Hamiltonian into the Dirac Hamiltonian coupled to a nontrivial gravitational field. Then we find that a gravitational curvature is induced at the vortex core, with its total flux quantized in integer multiples of $\pi$, reflecting the $\mathbb{Z}_2$ topology. Although the curvature vanishes everywhere except at the vortex core, the energy spectrum remains sensitive to the total curvature flux, owing to the gravitational Aharonov-Bohm effect. We further demonstrate that our gravitational framework can be applied to the topological phase transition driven by the vortex-linking precess in three-dimensional helical superconductors such as the He-B phase.

cond-mat.mes-hall↗

arXiv2025

Lattice Weyl Fermion on a Single Spherical Domain-Wall

We investigate a single spherical domain-wall embedded in a three-dimensional Euclidean lattice. We employ the Shamir-type domain-wall fermion formulation, where the negative mass region is confined inside the $S^2$ domain-wall, while the positive mass outside is taken to the infinite limit, allowing the exterior region to be neglected effectively. In the absence of a gauge potential, Weyl fermions emerge as edge-localized modes along the $S^2$ domain-wall. When a nontrivial $U(1)$ gauge potential is present, additional zero modes with opposite chirality appears, localized at the center near the monopole. This centrally localized mode originates from the effective mass contribution of the Wilson term, which induces a domain-wall near the monopole.

hep-lat↗

arXiv2024

A lattice formulation of Weyl fermions on a single curved surface

In the standard lattice domain-wall fermion formulation, one needs two flat domain-walls where both of the left- and right-handed massless modes appear. In this work we investigate a single domain-wall system with a nontrivial curved background. Specifically we consider a massive fermion on a $3D$ square lattice, whose domain-wall is a $2D$ sphere. In the free theory, we find that a single Weyl fermion is localized at the wall and it feels gravity through the induced spin connection. With a topologically nontrivial $U(1)$ link gauge field, however, we find a zero mode with the opposite chirality localized at the center where the gauge field is singular. In the latter case, the low-energy effective theory is not chiral but vectorlike. We discuss how to circumvent this obstacle in formulating lattice chiral gauge theory in the single domain-wall fermion system.

hep-lat↗

arXiv2024

Why magnetic monopole becomes dyon in topological insulators

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 continuum and numerically on a lattice, by adding the Wilson term and smearing the gauge field within a finite range to regularize the short-distance behavior of the system. Our results reveal that the Wilson term induces a strong positive mass shift, creating a domain-wall around the monopole/vortex. This small, yet finite-sized domain-wall localizes the chiral zero modes and ensures their stability through the Atiyah-Singer index theorem, whose cobordism invariance is crucial in explaining why the electric charge is fractional.

cond-mat.mes-hall↗

arXiv2024

Symmetry fractionalization and duality defects in Maxwell theory

We consider Maxwell theory on a non-spin manifold. Depending on the choice of statistics for line operators, there are three non-anomalous theories and one anomalous theory with different symmetry fractionalizations. We establish the gauging maps that connect the non-anomalous theories by coupling them to a discrete gauge theory. We also construct topological interfaces associated with $\mathrm{SL}(2,\mathbb{Z})$ duality and gauging of electric and magnetic one-form symmetries. Finally, by stacking the topological interfaces, we compose various kinds of duality defects, which lead to non-invertible symmetries of non-spin Maxwell theories.

hep-th↗

arXiv2024

A lattice regularization of Weyl fermions in a gravitational background

We report on a lattice fermion formulation with a curved domain-wall mass term to nonperturbatively describe fermions in a gravitational background. In our previous work in 2022, we showed under the time-reversal symmetry that the edge-localized massless Dirac fermion appears on one and two-dimensional spherical domain-walls and the spin connection is induced on the lattice in a consistent way with continuum theory. In this work, we extend our study to the Shamir type curved domain-wall fermions without the time-reversal symmetry. We find in the free fermion case that a single Weyl fermion appears on the edge, and feels gravity through the induced spin connection. With a topologically nontrivial $U(1)$ gauge potential, however, we find an oppositely chiral zero mode at the center where the gauge field is singular.

hep-lat↗

arXiv2024

A Microscopic study of Magnetic monopoles in Topological Insulators

In this article, we analyze a magnetic monopole in topological insulators. The monopole obtain a fractional electric charge because of the Witten effect. We consider this system with a microscopic view by adding the Wilson term to the ordinary Dirac Hamiltonian. The Wilson term yields the positive mass shift to the effective mass of the electrons, then the curved domain-wall is dynamically generated around the monopole. The zero-modes of the electrons are localized on the domain-wall, which can be identified as the source of the electric charge.

hep-lat↗

arXiv2024

Higher-group structure in lattice Abelian gauge theory under instanton-sum modification

We consider the $U(1)$ gauge theory on a four-dimensional torus, where the instanton number is restricted to an integral multiple of $p$. This theory possesses the nontrivial higher-group structure, which can be regarded as a generalization of the Green--Schwarz mechanism, between $\mathbb{Z}_q$ $1$-form and $\mathbb{Z}_{pq}$ $3$-form symmetries. Here, $\mathbb{Z}_q$ is a subgroup of the center of~$U(1)$. Following the recent study of the lattice construction of the $U(1)/\mathbb{Z}_q$ principal bundle, we examine how such a structure is realized on the basis of lattice regularization.

hep-th↗

arXiv2023

Higher-group symmetry in lattice gauge theories with restricted topological sectors

In this paper, we give a brief overview of generalized symmetries from the point of view of the lattice regularization as a fully regularized framework. At first, we illustrate the generalization of 't~Hooft anomaly matching for higher-form symmetries. Furthermore the main interest goes to the higher-group symmetry. In particular, we find that the so-called $4$-group appears in the lattice Yang--Mills theory under modification of instanton sum.

hep-lat↗

arXiv2022

Effective field theory in light of relative entropy

We study constraints on the effective field theory (EFT) from the relative entropy between two theories: we refer to these as target and reference theories. The consequence of the non-negativity of the relative entropy is investigated by choosing some reference theories for a given target theory involving field theories, quantum mechanical models, etc. It is found that the constraints on EFTs, e.g., the single massless scalar field with the dimension-eight operator, and SMEFT dimension-eight $SU(N)$ gauge bosonic operators, are consistent with the positivity bounds from the unitarity and causality when the higher-derivative operators are generated by the interaction between heavy and light fields. The constraints on Einstein-Maxwell theory with higher-derivative operators from the non-negativity of relative entropy are also investigated. The constraints on such EFTs from the relative entropy hold under an assumption that perturbative corrections from the interaction involving higher-derivative operators of light fields are not dominant in the EFTs. The consequence of this study on the weak gravity conjecture and the second law of thermodynamics is also discussed.

hep-th↗

arXiv2022

Violation of bound on chaos for charged probe in Kerr-Newman-AdS black hole

We investigate the conjectured bound on the Lyapunov exponent for a charged particle with angular motion in the Kerr-Newman-AdS black hole. The Lyapunov exponent is calculated based on the effective Lagrangian. We show that the negative cosmological constant reduces the chaotic behavior of the particle, namely, it decreases the Lyapunov exponent. Hence, the bound is more effective in the AdS spacetime than in the flat spacetime. Nevertheless, we find that the bound can be violated when the angular momenta of the black hole are turned on. Moreover, we show that in an extremal black hole, the bound is more easily violated compared to the nonextremal black hole.

gr-qc↗

arXiv2022

Bound on the Lyapunov exponent in Kerr-Newman black holes via a charged particle

We investigate the conjecture on the upper bound of the Lyapunov exponent for the chaotic motion of a charged particle around a Kerr-Newman black hole. The Lyapunov exponent is closely associated with the maximum of the effective potential with respect to the particle. We show that when the angular momenta of the black hole and particle are considered, the Lyapunov exponent can exceed the conjectured upper bound. This is because the angular momenta change the effective potential and increase the magnitude of the chaotic behavior of the particle. Furthermore, the location of the maximum is also related to the value of the Lyapunov exponent and the extremal and non-extremal states of the black hole.

gr-qc↗

arXiv2020

From 3d dualities to hadron physics

When one of the space-time dimension is compactified on $S^1$, the QCD exhibits the chiral phase transition at some critical radius. When we further turn on a background $θ$ term which depends on the $S^1$ compactified coordinate, a topological ordered phase appears at low energy via the winding of $θ$. We discuss what kind of theories can describe the physics near the critical point by requiring the matching of topological field theories in the infrared. As one of the possibilities, we propose a scenario where the $ρ$ and $ω$ mesons form a $U(N_f)$ gauge theory near the critical point. In the phase where the chiral symmetry is restored, they become the dual gauge boson of the gluon related by the level-rank duality between the three dimensional gauge theories, $SU(N)_{N_f}$ and $U(N_f)_{-N}$.

hep-th↗

arXiv2020

Half-hypermultiplets and incomplete/complete resolutions in F-theory

We consider resolutions of codimension-two enhanced singularities from $SO(12)$ to $E_7$ and from $E_7$ to $E_8$ in six-dimensional F-theory, where a half-hypermultiplet arises for generic complex structures achieving them. The exceptional fibers at the enhanced point exhibit different structures depending on how the colliding 7-brane approaches the stack of gauge 7-branes, as previously observed by Morrison and Taylor in the case of the enhancement from $SU(6)$ to $E_6$. When the colliding brane approaches them as $O(s)$, where $s$ is the coordinate of the base space along the gauge 7-branes, the resolution process ends up with fewer exceptional fibers than naively expected from the Kodaira classification, with a non-Dynkin intersection matrix including half-integral intersection numbers. We confirm that the exceptional fibers at the enhanced point form extremal rays of the cone of the positive weights of the relevant pseudo-real representation, explaining why a half-hypermultiplet arises there. By altering the ordering of the singularities blown up in the process, we obtain, for both $SO(12)\rightarrow E_7$ and $E_7\rightarrow E_8$, the intersection diagram on every other row of the corresponding box graphs. We present detailed derivations of the intersection diagrams of the exceptional fibers at the singularity enhanced points by examining how an exceptional curve is lifted up on the chart arising due to the subsequent blowing-up process. When the colliding brane approaches the stack of branes as $O(s^2)$, we obtain additional conifold singularity at the enhanced point, which completes the full Dynkin diagram of the enhanced group as was found previously.

hep-th↗

arXiv2019

More on a dessin on the base: Kodaira exceptional fibers and mutually (non-)local branes

A "dessin d'enfant" is a graph embedded on a two-dimensional oriented surface named by Grothendieck. Recently we have developed a new way to keep track of non-localness among 7-branes in F-theory on an elliptic fibration over $P^1$ by drawing a triangulated "dessin" on the base. To further demonstrate the usefulness of this method, we provide three examples of its use. We first consider a deformation of the $I_0^*$ Kodaira fiber. With a dessin, we can immediately find out which pairs of 7-branes are (non-)local and compute their monodromies. We next identify the paths of string(-junction)s on the dessin by solving the mass geodesic equation. By numerically computing their total masses, we find that the Hanany-Witten effect has not occurred in this example. Finally, we consider the orientifold limit in the spectral cover/Higgs bundle approach. We observe the characteristic configuration presenting the cluster sub-structure of an O-plane found previously.

hep-th↗

arXiv2019

A dessin on the base: a description of mutually non-local 7-branes without using branch cuts

We consider the special roles of the zero loci of the Weierstrass invariants $g_2(τ(z))$, $g_3(τ(z))$ in F-theory on an elliptic fibration over $P^1$ or a further fibration thereof. They are defined as the zero loci of the coefficient functions $f(z)$ and $g(z)$ of a Weierstrass equation. They are thought of as complex co-dimension one objects and correspond to the two kinds of critical points of a dessin d'enfant of Grothendieck. The $P^1$ base is divided into several cell regions bounded by some domain walls extending from these planes and D-branes, on which the imaginary part of the $J$-function vanishes. This amounts to drawing a dessin with a canonical triangulation. We show that the dessin provides a new way of keeping track of mutual non-localness among 7-branes without employing unphysical branch cuts or their base point. With the dessin we can see that weak- and strong-coupling regions coexist and are located across an $S$-wall from each other. We also present a simple method for computing a monodromy matrix for an arbitrary path by tracing the walls it goes through.

hep-th↗