Modular origin of mass hierarchy: Froggatt-Nielsen like mechanism

We study Froggatt-Nielsen (FN) like flavor models with modular symmetry. The FN mechanism is a convincing solution to the flavor puzzle in the quark sector. The FN mechanism requires an extra U(1) gauge symmetry which is broken at high energies. Alternatively, in the framework of modular symmetry the modular weights can play the role of the FN charges of the extra U(1) symmetry. Based on the FN-like mechanism with modular symmetry we present new flavor models for the quark sector. Assuming that the three generations have a common representation under the modular symmetry, our models simply reproduce the FN-like Yukawa matrices. We also show that the realistic mass hierarchy and mixing angles, which are related to each other through the modular parameters and a scalar vev, can be realized in models with several finite modular groups (and their double covering groups) without unnatural hierarchical parameters.

Double cover K3 surfaces of Hirzebruch surfaces

General K3 surfaces obtained as double covers of the n-th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.

Gushel--Mukai varieties: intermediate Jacobians

We describe intermediate Jacobians of Gushel-Mukai varieties $X$ of dimensions 3 or 5: if $A$ is the Lagrangian space associated with $X$, we prove that the intermediate Jacobian of $X$ is isomorphic to the Albanese variety of the canonical double covering of any of the two dual Eisenbud-Popescu-Walter surfaces associated with $A$. As an application, we describe the period maps for Gushel-Mukai threefolds and fivefolds. Comment: 48 pages. Latest addition to our series of articles on the geometry of Gushel-Mukai varieties; v2: minor stylistic improvements, results unchanged; v3: minor improvements; v4: final version, published in EPIGA

Modular symmetry by orbifolding magnetized T2 × T2: realization of double cover of ΓN

We study the modular symmetry of zero-modes on $$ {T}_1^2\times {T}_2^2 $$ T 1 2 × T 2 2 and orbifold compactifications with magnetic fluxes, M1, M2, where modulus parameters are identified. This identification breaks the modular symmetry of $$ {T}_1^2\times {T}_2^2 $$ T 1 2 × T 2 2 , SL(2, ℤ)1× SL(2, ℤ)2 to SL(2, ℤ) ≡ Γ. Each of the wavefunctions on $$ {T}_1^2\times {T}_2^2 $$ T 1 2 × T 2 2 and orbifolds behaves as the modular forms of weight 1 for the principal congruence subgroup Γ(N), N being 2 times the least common multiple of M1 and M2. Then, zero-modes transform each other under the modular symmetry as multiplets of double covering groups of ΓN such as the double cover of S4.

On the degenerate pin groups

We define a double covering homomorphism between a degenerate pin group and a degenerate orthogonal group which are given as semi-direct products. We also show that both of them are decomposed into four disjoint sets consisting of connected components. Then, using the components of pseudo-orthogonal group, we investigate the components of degenerate pin group and degenerate orthogonal group.

Flexible Temperature Sensor Integration into E-Textiles Using Different Industrial Yarn Fabrication Processes

Textiles enhanced with thin-film flexible sensors are well-suited for unobtrusive monitoring of skin parameters due to the sensors’ high conformability. These sensors can be damaged if they are attached to the surface of the textile, also affecting the textiles’ aesthetics and feel. We investigate the effect of embedding flexible temperature sensors within textile yarns, which adds a layer of protection to the sensor. Industrial yarn manufacturing techniques including knit braiding, braiding, and double covering were utilised to identify an appropriate incorporation technique. The thermal time constants recorded by all three sensing yarns was <10 s. Simultaneously, effective sensitivity only decreased by a maximum of 14% compared to the uncovered sensor. This is due to the sensor being positioned within the yarn instead of being in direct contact with the measured surface. These sensor yarns were not affected by bending and produced repeatable measurements. The double covering method was observed to have the least impact on the sensors’ performance due to the yarn’s smaller dimensions. Finally, a sensing yarn was incorporated in an armband and used to measure changes in skin temperature. The demonstrated textile integration techniques for flexible sensors using industrial yarn manufacturing processes enable large-scale smart textile fabrication.