Structure of stable degeneration of K3 surfaces into pairs of rational elliptic surfaces
Creators
- 1. KEK Theory Center, Institute of Particle and Nuclear Studies, KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)
Description
F-theory/heterotic duality is formulated in the stable degeneration limit of a K3 fibration on the F-theory side. In this note, we analyze the structure of the stable degeneration limit. We discuss whether stable degeneration exists for pairs of rational elliptic surfaces. We demonstrate that, when two rational elliptic surfaces have an identical complex structure, stable degeneration always exists. We provide an equation that systematically describes the stable degeneration of a K3 surface into a pair of isomorphic rational elliptic surfaces. When two rational elliptic surfaces have different complex structures, whether their sum glued along a smooth fiber admits deformation to a K3 surface can be determined by studying the structure of the K3 lattice. We investigate the lattice theoretic condition to determine whether a deformation to a K3 surface exists for pairs of extremal rational elliptic surfaces. In addition, we discuss the configurations of singular fibers under stable degeneration. The sum of two isomorphic rational elliptic surfaces glued together admits a deformation to a K3 surface, the singular fibers of which are twice that of the rational elliptic surface. For special situations, singular fibers of the resulting K3 surface collide and they are enhanced to a fiber of another type. Some K3 surfaces become attractive in these situations. We determine the complex structures and the Weierstrass forms of these attractive K3 surfaces. We also deduce the gauge groups in F-theory compactifications on these attractive K3 surfaces times a K3. , , , , and gauge groups arise in these compactifications.
Availability note (English)
Available from http://dx.doi.org/10.1007/JHEP03(2018)045; Available from http://repo.scoap3.org/record/24259Additional details
Identifiers
- DOI
- 10.1007/JHEP03(2018)045;
- arXiv
- arXiv:1710.04984;
Publishing Information
- Journal Title
- Journal of High Energy Physics (Online)
- Journal Volume
- 2018
- Journal Issue
- 03
- Journal Page Range
- p. 45
- ISSN
- 1029-8479
INIS
- Country of Publication
- Germany
- Country of Input or Organization
- International Atomic Energy Agency (IAEA)
- INIS RN
- 49090168
- Subject category
- S72: PHYSICS OF ELEMENTARY PARTICLES AND FIELDS;
- Descriptors DEI
- COMPACTIFICATION; DIFFERENTIAL GEOMETRY; DUALITY; FIBERS; GAUGE INVARIANCE; SU-5 GROUPS; SUPERSTRING MODELS; SUPERSTRING THEORY
- Descriptors DEC
- COMPOSITE MODELS; EXTENDED PARTICLE MODEL; GEOMETRY; INVARIANCE PRINCIPLES; LIE GROUPS; MATHEMATICAL MODELS; MATHEMATICS; M-THEORY; PARTICLE MODELS; QUARK MODEL; STRING MODELS; STRING THEORY; SU GROUPS; SYMMETRY GROUPS
Optional Information
- Copyright
- Copyright (c) OPEN ACCESS, © The Authors
- Notes
- PUBLISHER-ID: JHEP03(2018)045; ARXIV:1710.04984; OAI: oai:repo.scoap3.org:24259
- Funding organization
- SCOAP3, CERN, Geneva (Switzerland)