Heterotic strings on T3/ℤ2, Nikulin involutions and M-theory

• Published in: The journal of high energy physics Vol. 2022; no. 9; p. 209
• Main Authors: Acharya, Bobby Samir, Aldazabal, Gerardo, Font, Anamaría, Narain, Kumar, Zadeh, Ida G.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 26-09-2022; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Field theory; High energy physics; M theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supergravity; Supersymmetry; Superstring Vacua; Superstrings and Heterotic Strings; Conformal Field Models in String Theory; M-Theory
• ISSN: 1029-8479
• DOI: 10.1007/JHEP09(2022)209

A
bstract
We first describe the low energy dynamics of ten dimensional heterotic supergravity compactified on the smooth, flat 3-manifold
T
3
/ℤ
2
, without supersymmetry, and explain how it arises from flat heterotic gauge fields. The semi-classical theory has both Coulomb and Higgs branches of non-supersymmetric vacua. We then give an exact worldsheet description as asymmetric orbifolds of
T
3
, where the orbifold generator involves a Nikulin non-symplectic involution
θ
of the even self-dual lattice Γ
(19
,
3)
. Along the way we briefly compare our findings with M-theory on K3
/θ
. Our construction gives a novel CFT description of the semi-classical field theory moduli space. In particular, the Wilson line parameters in the lattice
I
⊂ Γ
(19
,
3)
of signature (19
− s,
1) which is invariant under
θ
, and in its orthogonal complement
N
, correspond respectively to Coulomb and Higgs branch moduli. There is a rich pattern of transitions amongst Higgs and Coulomb branches which we describe using the worldsheet theory.