Finite Groups for the Kummer Surface: the Genetic Code and a Quantum Gravity Analogy

Groupes finis pour la surface de Kummer: le code génétique et une analogie à la gravité quantique

Michel Planat (1) , David Chester , Raymond Aschheim (2) , Marcelo M Amaral (2) , Fang Fang , Klee Irwin (2)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
2 Quantum Gravity Research - Quantum Gravity Research

The Kummer surface was constructed in 1864. It corresponds to the desingularization of the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in some models of quantum gravity. Following our recent model of the DNA genetic code based on the irreducible characters of the finite group G5:=(240,105)≅Z5⋊2O (with 2O the binary octahedral group), we now find that groups G6:=(288,69)≅Z6⋊2O and G7:=(336,118)≅Z7⋊2O can be used as models of the symmetries in hexamer and heptamer proteins playing a vital role for some biological functions. Groups G6 and G7 are found to involve the Kummer surface in the structure of their character table. An analogy between quantum gravity and DNA/RNA packings is suggested.

Mots clés: 10.3390/quantum3010005

Domaines: Théorie des groupes [math.GR]; Géométrie algébrique [math.AG]; Physique [physics]; Physique Quantique [quant-ph]; Génétique; Relativité Générale et Cosmologie Quantique [gr-qc]

Michel Planat, David Chester, Raymond Aschheim, Marcelo M Amaral, Fang Fang, et al.. Finite Groups for the Kummer Surface: the Genetic Code and a Quantum Gravity Analogy. Quantum Reports, 2021, 3 (1), pp.68-79. ⟨10.3390/quantum3010005⟩. ⟨hal-03100697⟩