Tootfinder

Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras
Hsian-Yang Chen, Ching Hung Lam
https://arxiv.org/abs/2402.13621

Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras
We continue our study of cyclic orbifolds of lattice vertex operator algebras and their full automorphism groups. We consider some special isometry $g\in O(L)$ such that $g^i$ is fixed point free on $L$ for any $1\leq i\leq |g|-1$. We show that when $L_2=\emptyset$ and $g^i$ is fixed point free on $L$ for any $1\leq i\leq |g|-1$, $V_L^{\hat{g}}$ has extra automorphisms implies either (1) the order of $g$ is a prime or (2) $L$ is isometric to the Leech lattice or some coinvar…

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Collective nature of high-Q resonances in finite-size photonic metastructures
Thanh Xuan Hoang, Daniel Leykam, Hong-Son Chu, Ching Eng Png, Francisco J. Garc{\i}a-Vidal, Yuri S. Kivshar
https://arxiv.org/abs/2405.01034

Collective nature of high-Q resonances in finite-size photonic metastructures
We study high quality-factor (high Q) resonances supported by periodic arrays of Mie resonators from the perspectives of both Bloch wave theory and multiple scattering theory. We reveal that, unlike a common belief, the bound states in the continuum (BICs) derived by the Bloch-wave theory do not directly determine the resonance with the highest Q value in large but finite arrays. Higher Q factors appear to be associated with collective resonances formed by nominally guided modes below the light…

Automorphism groups of parafermion vertex operator algebras: general case
Ching Hung Lam, Xingjun Lin, Hiroki Shimakura
https://arxiv.org/abs/2404.17096 ht…

Automorphism groups of parafermion vertex operator algebras: general case
We complete the program for determining the full automorphism groups of all parafermion vertex operator algebras associated with simple Lie algebras and positive integral levels. We show that the full automorphism group of the parafermion vertex operator algebra is isomorphic to the automorphism group of the associated root system for the remaining cases: (i) the level is at least $3$; (ii) the level is $2$ and the simple Lie algebra is non simply laced.