Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities

Autor(en)

Cesar Fierro Cota, Albrecht Klemm, Thorsten Schimannek

Abstrakt

We calculate the generating functions of BPS indices using their modular properties in Type II and M-theory compactifications on compact genus one fibered CY 3-folds with singular fibers and additional rational sections or just N -sections, in order to study string dualities in four and five dimensions as well as rigid limits in which gravity decouples. The generating functions are Jacobi-forms of Γ

₁(N) with the complexified fiber volume as modular parameter. The string coupling λ, or the ϵ

_± parameters in the rigid limit, as well as the masses of charged hypermultiplets and non-Abelian gauge bosons are elliptic parameters. To understand this structure, we show that specific auto-equivalences act on the category of topological B-branes on these geometries and generate an action of Γ

₁(N) on the stringy Kähler moduli space. We argue that these actions can always be expressed in terms of the generic Seidel-Thomas twist with respect to the 6-brane together with shifts of the B-field and are thus monodromies. This implies the elliptic transformation law that is satisfied by the generating functions. We use Higgs transitions in F-theory to extend the ansatz for the modular bootstrap to genus one fibrations with N -sections and boundary conditions fix the all genus generating functions for small base degrees completely. This allows us to study in depth a wide range of new, non-perturbative theories, which are Type II theory duals to the CHL ℤ

_N orbifolds of the heterotic string on K3 × T

₂. In particular, we compare the BPS degeneracies in the large base limit to the perturbative heterotic one-loop amplitude with R+2F+2g−2 insertions for many new Type II geometries. In the rigid limit we can refine the ansatz and obtain the elliptic genus of superconformal theories in 5d.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Rheinische Friedrich-Wilhelms-Universität Bonn

Journal

Journal of High Energy Physics

Band

2019

Anzahl der Seiten

96

ISSN

1029-8479

DOI

https://doi.org/10.1007/JHEP11(2019)170

Publikationsdatum

11-2019

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Nuclear and High Energy Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/b8ebd933-0b3f-4594-96d9-cbef29b6d488