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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., Comment: 38 pages, 5 figures

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., Comment: 26 pages, 12 figures, minor corrections, published version

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., Comment: 9 pages, contribution to the 40th International Symposium on Lattice Field Theory (Lattice2023), July 31st - August 4th, 2023, Fermi National Accelerator Laboratory

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., Comment: 9 pages, 6 figures. Talk presented at the 40th International Symposium on Lattice Field Theory (Lattice2023), 31 July - 4 August 2023, Fermi National Accelerator Laboratory, minor corrections

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., Comment: 7 pages, 3 figures, talk presented at the 40th International Symposium on Lattice Field Theory (Lattice2023), July 31st - August 4th, 2023, Fermi National Accelerator Laboratory

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., Comment: 40 pages, 10 figures, minor corrections, references added, published version

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., Comment: 16 pages, to appear in EPJC. In Sect. 2, our discussions in continuum theory were falsely attributed to the periodicity of the compact scalar and have been corrected. These modifications do not modify any conclusion in lattice theory

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., Comment: 94 pages, 6 figures

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., Comment: 22 pages, 42 figures

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., Comment: 25 pages, 6 figures, published in PRD

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., Comment: 50 pages, 16 figures, v2: minor corrections

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., Comment: 16 pages, 9 figures

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 $\theta$ term which depends on the $S^1$ compactified coordinate, a topological ordered phase appears at low energy via the winding of $\theta$. 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 $\rho$ and $\omega$ 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 $U(N_f)_{-N}$., Comment: 40 pages, 2 figures, version to appear in PRD

We consider the special roles of the zero loci of the Weierstrass invariants $g_2(\tau(z))$, $g_3(\tau(z))$ 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., Comment: 27 pages, 9 figures. v3: Title changed, section 3 added to explain the notion of a "dessin d'enfant", sections 4,6 and 7 in v2 removed

We prove, by a direct dimensional reduction and an explicit construction of the group manifold, that the nonlinear sigma model of the dimensionally reduced three-dimensional A = R magical supergravity is F4(+4)/(USp(6)xSU(2)). This serves as a basis for the solution generating technique in this supergravity as well as allows to give the Lie algebraic characterizations to some of the parameters and functions in the original D = 5 Lagrangian. Generalizations to other magical supergravities are also discussed., Comment: 15 pages