arXiv subjects

Yamato Honda

Publications and source records attributed to Yamato Honda.

7 recordsLinked to original sources

arXiv2026

Maximal Enhancements in Eight-Dimensional Non-Supersymmetric Heterotic Strings

We classify maximally enhanced, rank-preserving non-supersymmetric heterotic strings in eight dimensions by studying orbifolds of supersymmetric heterotic strings on $T^2$. We first review the construction in nine dimensions, where it reproduces the $95$ maximally semisimple enhancement points obtained from previous extended-Dynkin analyses. We then start from the maximally enhanced supersymmetric Narain points in eight dimensions and use Kac's theorem to enumerate candidate order-two inner actions, retaining only those that lift to consistent Narain-lattice shifts. This gives $1210$ maximal enhancement points, of which $71$ are tachyon-free, and $25$ have neither tachyons nor shifted-sector massless scalars. For each entry we determine the gauge algebra and the low-lying scalar and fermion spectra, and for the tachyon-free cases we evaluate the one-loop cosmological constant. For the 25 subcases without shifted-sector massless scalars, we further compute the Hessian of the one-loop potential and test the refined de Sitter swampland conjecture.

hep-th↗

arXiv2026

Parafermionizing the Monster

We study the parafermionization of the Monster CFT with respect to its $\mathbb{Z}_{pA}$ subgroups, with $p$ an odd prime. Under certain assumptions, we show that the parafermionization is equal to a non-invertible gauging of $\mathcal{P}(p) \times \mathcal{P}(p)^\vee$, where $\mathcal{P}(p)$ is the theory of $\mathbb{Z}_p$-parafermions and $\mathcal{P}(p)^\vee$ is an appropriate dual theory, with global symmetry characterized by the centralizer of $\mathbb{Z}_{pA}$. By tracking the symmetries of $\mathcal{P}(p) \times \mathcal{P}(p)^\vee$ through the non-invertible gauging, we argue that the diagonal Monster CFT has $\mathrm{Rep}(\mathfrak{so}(3)_p) \boxtimes \mathrm{Rep}(\mathfrak{so}(3)_p)^\mathrm{op}$ symmetry, and hence that the holomorphic Monster theory has symmetry $\mathrm{Rep}(\mathfrak{so}(3)_p)$. We then compute the defect McKay-Thompson series associated to these symmetries, and prove that their invariance subgroups are $Γ_1(p+2)$.

hep-th↗

arXiv2026

Haagerup Symmetry in $(E_8)_1$?

We suggest that the chiral $(\mathfrak{e}_8)_1$ theory -- in many senses the simplest VOA -- may have Haagerup symmetry $\mathcal{H}_i$ for $i=1,2,3$. Likewise, we suggest that the non-chiral $(E_8)_1$ WZW model may have $\mathcal{H}_i \times \mathcal{H}_i^\textrm{op}$ symmetry, and that gauging the diagonal symmetry gives a $c=8$ theory with $\mathcal{Z}(\mathcal{H}_3)$ symmetry, which is the theory predicted in \cite{Evans:2010yr}. Along the way, we show that $(E_8)_1$ also has a $\mathrm{Fib} \times \mathrm{Fib}^\text{op}$ symmetry, and that gauging the diagonal symmetry gives the $(G_2)_1 \times (F_4)_1$ WZW model, explaining the well-known conformal embedding $(G_2)_1 \times (F_4)_1 \subset (E_8)_1$. Finally, we suggest a relation to theories with $\mathcal{H}_3$ symmetry at $c=2,6$, complimenting the discussion with new modular bootstrap results.

hep-th↗

arXiv2024

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry

We investigate the non-invertible symmetry associated with chiral symmetry in axion quantum electrodynamics (QED) using the modified Villain formulation. In axion QED, it is known that naive magnetic objects such as 't Hooft loops and axion strings lose their gauge invariance due to the violation of the Bianchi identity for the field strength of the photon or "field strength" of the axion. First, we construct the action of axion QED on the square lattice, which is more intricate than its counterpart in the continuum theory. We then observe the breaking of gauge invariance. Subsequently, we construct gauge-invariant magnetic objects by introducing new degrees of freedom localized at the positions of the magnetic objects. Furthermore, we explicitly compute the response of the magnetic objects under the action of the non-invertible symmetry operator constructed in Ref. [1]. In this analysis, we employ a method different from the so-called half-space gauging, which is the standard method to study non-invertible symmetries.

hep-lat↗

arXiv2024

Action of the axial $U(1)$ non-invertible symmetry on the 't~Hooft line operator: A simple argument

Employing the modified Villain lattice formulation of the axion quantum electrodynamics, we present an alternative and much simpler derivation of the conclusion of~Ref.~\cite{Honda:2024sdz} that the sweep of the axial $U(1)$ non-invertible symmetry operator over the (non-genuine) gauge invariant 't~Hooft line operator with an integer magnetic charge does not leave any effect. The point is that such a 't~Hooft line can be represented by a boundary of a (non-topological) defect that is invariant under the axial transformation on the axion field.

hep-lat↗

arXiv2024

Action of the axial $U(1)$ non-invertible symmetry on the 't~Hooft line operator: A lattice gauge theory study

We study how the symmetry operator of the axial $U(1)$ non-invertible symmetry acts on the 't~Hooft line operator in the $U(1)$ gauge theory by employing the modified Villain-type lattice formulation. We model the axial anomaly by a compact scalar boson, the ``QED axion''. For the gauge invariance, the simple 't~Hooft line operator, which is defined by a line integral of the dual $U(1)$ gauge potential, must be ``dressed'' by the scalar and $U(1)$ gauge fields. A careful consideration on the basis of the anomalous Ward--Takahashi identity containing the 't~Hooft operator with the dressing factor and a precise definition of the symmetry operator on the lattice shows that the symmetry operator leaves no effect when it sweeps out a 't~Hooft loop operator. This result appears inequivalent with the phenomenon concluded in the continuum theory. In an appendix, we demonstrate that the half-space gauging of the magnetic $\mathbb{Z}_N$ 1-form symmetry, when formulated in an appropriate lattice framework, leads to the same conclusion as above. A similar result is obtained for the axion string operator.

hep-lat↗

arXiv2024

Lattice realization of the axial $U(1)$ noninvertible symmetry

In $U(1)$ lattice gauge theory with compact $U(1)$ variables, we construct the symmetry operator, i.e.\ the topological defect, for the axial $U(1)$ noninvertible symmetry. This requires a lattice formulation of chiral gauge theory with an anomalous matter content and we employ the lattice formulation on the basis of the Ginsparg--Wilson relation. The invariance of the symmetry operator under the gauge transformation of the gauge field on the defect is realized, imitating the prescription by Karasik in continuum theory, by integrating the lattice Chern--Simons term on the defect over \emph{smooth\/} lattice gauge transformations. The projection operator for allowed magnetic fluxes on the defect then emerges with lattice regularization. The resulting symmetry operator is manifestly invariant under lattice gauge transformations. In an appendix, we give another way of constructing the symmetry operator on the basis of a 3D $\mathbb{Z}_N$ topological quantum field theory, the level-$N$ BF theory on the lattice.

hep-lat↗