arXiv subjects

Ippo Orii

Publications and source records attributed to Ippo Orii.

5 recordsLinked to original sources

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 $\Gamma_1(p+2)$.

hep-th↗

arXiv2026

Web of dualities on non-orientable surfaces

It is known that a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry can be fermionized. Recent work shows that if the bosonic theory also has non-anomalous time-reversal symmetry, fermionization extends to non-orientable surfaces and yields a fermionic theory that depends on a $\mathrm{Pin}^-$ structure. Besides fermionization, one can define various topological manipulations, such as gauging and stacking invertible phases, which together generate a web of dualities. We prove that their group structure is the dihedral group $D_8$ of order 16. Furthermore, we systematically investigate the web from two perspectives: Symmetry TFT and actions on sectors of the $S^1$ Hilbert space.

hep-th↗

arXiv2025

Vanishing of the $H^3$ obstruction for time-reversal symmetry in (2+1)D abelian bosonic TQFTs

In $(2+1)$-dimensional topological quantum field theories (TQFTs), the action of a global symmetry group on the anyon system is one of the central topics of research. Owing to the subtle categorical nature of anyons, a global symmetry acting on them is generally realized in a projective manner. Symmetry fractionalization encodes this projective realization. The obstruction to defining symmetry fractionalization is captured by a cohomology class, known as the $H^3$ obstruction, whose nontriviality signals a failure to define symmetry fractionalization consistently. In this short note, we prove that the $H^3$ obstruction for time-reversal symmetry always vanishes in abelian bosonic TQFTs.

hep-th↗

arXiv2025

Generalization of anomaly formula for time reversal symmetry in (2+1)D abelian bosonic TQFTs

We study time-reversal symmetry in $(2+1)$D abelian bosonic topological phases. Time-reversal anomalies in such systems are classified by $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-protected topological (SPT) phases in $(3+1)$D, and can be diagnosed via partition functions on manifolds such as $\mathbb{RP}^4$ and $\mathbb{CP}^2$. These partition functions are related by the anomaly formula \begin{equation*} Z(\mathbb{RP}^4)\, Z(\mathbb{CP}^2) = \theta_{\mathcal{M}}, \end{equation*} where $\theta_\mathcal{M}$ is the Dehn twist phase associated with the crosscap state. Meanwhile, the existence of gapped boundaries is constrained by so-called higher central charges $\xi_n$, which serve as computable invariants encoding obstruction data. Motivated by the known relation $Z(\mathbb{CP}^2) = \xi_1$, we propose a generalization of the anomaly formula that involves both the higher central charges $\xi_n$ and a new time-reversal invariant $\eta_n$. Introducing a distinguished subset $\mathcal{M}^n \subset \mathcal{A}$ of anyons, we establish the relation \begin{equation*} \eta_n \cdot \xi_n = \frac{\sum_{a \in \mathcal{M}^n} \theta(a)^n}{\left| \sum_{a \in \mathcal{M}^n} \theta(a)^n \right|}, \end{equation*} which generalizes the known anomaly formula. We analyze the algebraic structure of $\mathcal{M}^n$, derive consistency relations it satisfies, and clarify its connection to the original anomaly formula.

hep-th↗

arXiv2025

On dimensions of (2+1)D abelian bosonic topological systems on non-orientable manifolds

We give a framework to describe abelian bosonic topological systems with parity symmetry on a torus in terms of the projective representation of $GL(2,\mathbb{Z})$. However, this information alone does not guarantee that we can assign Hilbert spaces to non-orientable surfaces in a way compatible with the gluing axiom of topological quantum field theory. Here, we show that we may assign Hilbert spaces with integer dimensions to non-orientable surfaces in the case of abelian bosonic topological systems with time-reversal symmetry, which can be seen as a necessary condition for the existence of topological quantum field theories.

hep-th↗