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

Cesar Cota (Bethe Center for Theoretical Physics, Universität Bonn, Bonn, D-53115, Germany) ; Albrecht Klemm (Bethe Center for Theoretical Physics, Universität Bonn, Bonn, D-53115, Germany; Hausdorff Center for Mathematics, Universität Bonn, Bonn, D-53115, Germany) ; Thorsten Schimannek (Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna, A-1090, Austria)

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 Γ1(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 Γ1(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 + 2 F + 2 g 2 $$ {R}_{+}^2{F}_{+}^{2g-2} $$ 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.

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      "surname": "Schimannek", 
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  "abstracts": [
    {
      "source": "Springer", 
      "value": "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 \u03931(N) with the complexified fiber volume as modular parameter. The string coupling \u03bb, or the \u03f5\u00b1 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 \u03931(N) on the stringy K\u00e4hler 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 \u2124 N  orbifolds of the heterotic string on K3 \u00d7 T 2. In particular, we compare the BPS degeneracies in the large base limit to the perturbative heterotic one-loop amplitude with   <math> <msubsup> <mi>R</mi> <mo>+</mo> <mn>2</mn> </msubsup> <msubsup> <mi>F</mi> <mo>+</mo> <mrow> <mn>2</mn> <mi>g</mi> <mo>\u2212</mo> <mn>2</mn> </mrow> </msubsup> </math>  $$ {R}_{+}^2{F}_{+}^{2g-2} $$  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."
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Published on:
28 November 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2019 (2019)
Issue 11
Pages 1-96
DOI:
https://doi.org/10.1007/JHEP11(2019)170
arXiv:
1910.01988
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: