Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

• Published in: The journal of high energy physics Vol. 2017; no. 7; pp. 1 - 22
• Main Authors: Braun, Volker, Cvetič, Mirjam, Donagi, Ron, Poretschkin, Maximilian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2017; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Conformal Field Models in String Theory; Discrete Symmetries; Elementary Particles; High energy physics; Manifolds (mathematics); Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Field Theory; String Theory; Symmetry; Torsion; Discrete Symmetries; String Field Theory; Conformal Field Models in String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2017)129

A bstract We provide the first explicit example of Type IIB string theory compactification on a globally defined Calabi-Yau threefold with torsion which results in a four-dimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of ℤ 2 × ℤ 2 . Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of second cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the cfour-dimensional theory.