We apply non-invertible selection rules coming from a fusion algebra to radiative neutrino mass models where fields are labeled by the elements in the algebra. Since non-invertible selection rules only hold at tree level, radiative corrections naturally explain the origin of tiny neutrino masses. Furthermore, a remnant symmetry of the fusion algebra protects the stability of dark matter, which is conventionally imposed in radiative neutrino models. We also find that interesting neutrino mass textures are realized by assigning fields to family-dependent elements in the algebra.

Japan

Tatsuo Kobayashi

China

Hiroshi Okada

Hajime Otsuka

Radiative neutrino mass models from non-invertible selection rules

<p>We study fermion zero-mode wave functions with various chiralities in the magnetized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>T</mi><mrow><mn>2</mn><mi>g</mi></mrow></msup></math>, (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>g</mi><mo>=</mo><mn>2</mn></mrow><mo>,</mo><mn>3</mn></mrow></math>), torus. First, we consider the wave functions satisfying the Dirac equation and the boundary conditions on the magnetized torus. Second, we introduce the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> (or parity) transformations and derive the wave functions under the modular transformation. Additionally, we calculate the Yukawa couplings taking chirality into account. Lastly, we briefly review how to construct the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>T</mi><mn>4</mn></msup><mo>/</mo><msub><mi mathvariant="double-struck">Z</mi><mi>N</mi></msub></math>, (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn></mrow></math>), and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>T</mi><mn>6</mn></msup><mo>/</mo><msub><mi mathvariant="double-struck">Z</mi><mn>12</mn></msub></math> twisted orbifold. Also, we explicitly analyze the number of the wave functions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mi>N</mi></msub></math> sectors.</p>

Tim Jeric

Kaito Nasu

Shohei Takada

Generation structures and Yukawa couplings in magnetized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn><mi>g</mi></mrow></msup><mo>/</mo><msub><mrow><mi mathvariant="double-struck">Z</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math> models

We study coupling selection rules of chiral matter fields in heterotic string theory with standard embedding. These selection rules are determined by topological properties of Calabi-Yau threefolds. We classify coupling selection rules on complete intersection Calabi-Yau threefolds for $\textit{h}$ ≤ 5. It is found that all of these selection rules for $\textit{h}$ ≤ 5 are understood by combinations of only five types of fusion rules.

Jun Dong

Ryusei Nishida

Satsuki Nishimura

Coupling selection rules in heterotic Calabi-Yau compactifications

We study the lepton mass textures, which are derived by $\textit{ℤ}$ gauging of $\textit{ℤ}$ symmetries. We can obtain various textures for the Yukawa couplings in the charged lepton sector, but the patterns of neutrino mass matrices are limited. All the obtained textures can not be realized by group-theoretical symmetries, and certain textures can lead to realistic results.

Morimitsu Tanimoto

Haruki Uchida

Lepton mass textures from non-invertible multiplication rules

We study the coupling selection rules associated with non-group symmetries, i.e., ℤ gauging of ℤ symmetries. We clarify which Yukawa textures can be derived by our selection rules for $\textit{M}$ = 3$\textit{,}$ 4, and 5, and obtain various textures including the nearest neighbor interaction type and its extension. Some of them cannot be realized by a conventional group-like symmetry. They lead to interesting phenomenology such as a solution to the strong CP problem without axion.

Yume Nishioka

More about quark Yukawa textures from selection rules without group actions

We study the moduli stabilization by the radiative corrections due to the moduli dependent vector-like masses invariant under the finite modular symmetry. The radiative stabilization mechanism can stabilize the modulus $\textit{τ}$ of the finite modular symmetry Γ ($\textit{N}$ ∈ ℕ) at Im $\textit{τ}$ ≫ 1, where the shift symmetry $\textit{τ → τ}$ + 1 remains unbroken approximately. The shift symmetry can be considered as the residual ℤ symmetry which realizes the Froggatt-Nielsen mechanism with the hierarchy parameter $\textit{e}$ ≪ 1. In this work, we study the stabilization of multiple moduli fields, so that various hierarchical values of the modular forms coexist in a model. For example, one modulus stabilized at Im $\textit{τ}$ ∼ 3 is responsible for the hierarchical structure of the quarks and leptons in the Standard Model, and another modulus stabilized at Im $\textit{τ}$ ∼ 15 can account for the flatness of the Re $\textit{τ}$ direction which may be identified as the QCD axion.

Tetsutaro Higaki

South Korea

Junichiro Kawamura

Riku Sakuma

Large and small hierarchies from finite modular symmetries

We discuss selection rules of chiral matters in type IIA intersecting and IIB magnetized D-brane models on toroidal orbifolds. Since the chiral matters on toroidal orbifolds are labeled by a certain conjugacy class of the gauged orbifold group, the selection rules involve non-trivial fusion rules. We find that the representation of the chiral matters is described by a $\textit{D}$ flavor symmetry for an even number of magnetic fluxes or winding numbers at tree level. Furthermore, the $\textit{D}$ symmetry still remains even when we take into account loop effects. We also study non-perturbative effects such as D-brane instantons.

Shuta Funakoshi

Quantum aspects of non-invertible flavor symmetries in intersecting/magnetized D-brane models

We discuss the stabilization of multiple moduli by utilizing Siegel modular forms in the framework of Sp(2 , ℤ) modular invariant theories. For a generic modular- and CP-invariant scalar potential, we find that CP-conserving fixed points are stationary points. For concreteness, the stabilization of multiple moduli is explicitly demonstrated in Sp(4, ℤ) and Sp(6, ℤ) modular invariant scalar potentials. Furthermore, it turns out that there exists a light axion when the moduli are stabilized nearby a fixed point.

Moduli stabilization and light axion by Siegel modular forms

We study the vacua of modulus potentials consisting of multiple contributions of modular forms in a finite modular symmetry. If the potential is given by a single modular form, the Minkowski vacuum is realized at the fixed point of the modular symmetry. We show that the de Sitter vacuum is realized with a multiple modular form case and obtain a nontrivial vacuum away from the fixed point, i.e. a large modulus vacuum expectation value, depending on the choice of the weight and representation of the modular forms. We study these vacua numerically and analytically. It is also found that the vacua obtained in this paper preserve CP symmetry.

United States

Yoshihiko Abe

Komei Goto

Modulus Stabilization in Finite Modular Symmetric Models

Phenomenological aspects of non-invertible symmetries, in particular the flavor structure of quarks and leptons, are studied. We start with a ℤ M  discrete symmetry and gauge ℤ2 so as to obtain a non-invertible symmetry. We study which Yukawa textures can be derived from the non-invertible symmetries. Various textures can be realized and some of them cannot be realized by a conventional symmetry. For example, the nearest neighbor interaction texture as well as other interesting textures of quarks and leptons are obtained.