Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

Cvetič, Mirjam; Grassi, Antonella; Poretschkin, Maximilian

doi:10.1007/JHEP06(2017)156

Title: Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

Abstract

We study aspects of Heterotic/F-theory duality for compacti cations with Abelian discrete gauge symmetries. We consider F-theory compacti cations on genus-one bered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group Z_n. Such models are obtained by studying rst a speci c toric set-up whose associated Heterotic vector bundle has structure group Z_n. By employing a conjectured Heterotic/Ftheory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compacti cations to six dimensions. We provide explicit constructions of mirrorpairs for symmetric examples with Z₂ and Z₃, in six dimensions. The Heterotic models with symmetric discrete symmetries are related in eld theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stuckelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of brations with torsional sections and those with multi-sections.

Authors:

Cvetič, Mirjam ^[1]; Grassi, Antonella ^[2]; Poretschkin, Maximilian ^[3]

Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy; Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Mathematics; Univ. of Maribor, Maribor (Slovenia)
Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Mathematics
Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy

Publication Date:: Fri Jun 30 00:00:00 EDT 2017

Research Org.:: Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1425672

Grant/Contract Number:: SC0013528

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 6; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; Discrete Symmetries; F-theory; String Duality; Superstrings; Heterotic Strings

Citation Formats


                    Cvetič, Mirjam, Grassi, Antonella, and Poretschkin, Maximilian. Discrete symmetries in Heterotic/F-theory duality and mirror symmetry.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP06(2017)156.

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                    Cvetič, Mirjam, Grassi, Antonella, & Poretschkin, Maximilian. Discrete symmetries in Heterotic/F-theory duality and mirror symmetry.  United States.  https://doi.org/10.1007/JHEP06(2017)156

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                    Cvetič, Mirjam, Grassi, Antonella, and Poretschkin, Maximilian. Fri .  
"Discrete symmetries in Heterotic/F-theory duality and mirror symmetry".  United States.  https://doi.org/10.1007/JHEP06(2017)156.  https://www.osti.gov/servlets/purl/1425672.

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@article{osti_1425672,

  title        = {Discrete symmetries in Heterotic/F-theory duality and mirror symmetry},

  author       = {Cvetič, Mirjam and Grassi, Antonella and Poretschkin, Maximilian},

  abstractNote = {We study aspects of Heterotic/F-theory duality for compacti cations with Abelian discrete gauge symmetries. We consider F-theory compacti cations on genus-one bered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group Zn. Such models are obtained by studying rst a speci c toric set-up whose associated Heterotic vector bundle has structure group Zn. By employing a conjectured Heterotic/Ftheory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compacti cations to six dimensions. We provide explicit constructions of mirrorpairs for symmetric examples with Z2 and Z3, in six dimensions. The Heterotic models with symmetric discrete symmetries are related in eld theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stuckelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of brations with torsional sections and those with multi-sections.},

  doi          = {10.1007/JHEP06(2017)156},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 6,

  volume       = 2017,

  place        = {United States},

  year         = {Fri Jun 30 00:00:00 EDT 2017},

  month        = {Fri Jun 30 00:00:00 EDT 2017}

}

Copy to clipboard

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Works referencing / citing this record:

High U(1) charges in type IIB models and their F-theory lift
journal, April 2019

Cianci, Francesco Mattia; Mayorga Peña, Damián K.; Valandro, Roberto
Journal of High Energy Physics, Vol. 2019, Issue 4
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Non-vanishing Heterotic Superpotentials on Elliptic Fibrations
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Buchbinder, Evgeny I.; Lin, Ling; Ovrut, Burt A.
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Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
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Kimura, Yusuke
arXiv
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High U(1) charges in type IIB models and their F-theory lift
preprint, January 2018

Cianci, Francesco Mattia; Pena, Damian Kaloni Mayorga; Valandro, Roberto
arXiv
DOI: 10.48550/arxiv.1811.11777

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Title: Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

Abstract

Citation Formats

Weierstrass models of elliptic toric $K3$ hypersurfaces and symplectic cuts journal, January 2013

Mirror symmetry for lattice polarizedK3 surfaces journal, September 1996

Refined stable pair invariants for E-, M- and [p, q]-strings journal, November 2013

General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure journal, November 2015

F-theory with quantized fluxes journal, January 1999

Non-simply-connected gauge groups and rational points on elliptic curves journal, July 1998

Prepotentials from symmetric products journal, January 1999

Quartic gauge couplings from $K3$ geometry journal, January 1999

Vector Bundles and F Theory journal, August 1997

Aspects of the hypermultiplet moduli space in string duality journal, April 1998

Loop-corrected compactifications of the heterotic string with line bundles journal, June 2005

Picard Group of Hypersurfaces in Toric 3-Folds journal, February 2012

Discrete gauge symmetries by Higgsing in four-dimensional F-theory compactifications journal, December 2014

Elliptic fibrations with rank three Mordell-Weil group: F-theory with U(1)×U(1)×U(1) gauge symmetry journal, March 2014

Prepotential, mirror map and $F$-theory on $K3$ journal, January 1998

Complete classification of reflexive polyhedra in four dimensions journal, January 2000

On type IIB vacua with varying coupling constant journal, October 1999

F-theory on all toric hypersurface fibrations and its Higgs branches journal, January 2015

Compactifications of F-theory on Calabi-Yau threefolds (II) journal, September 1996

Mordell-Weil torsion in the mirror of multi-sections journal, December 2016

F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds journal, October 2012

F-theory on genus-one fibrations journal, August 2014

F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections journal, June 2013

Geometric singularities and enhanced gauge symmetries journal, December 1996

On discrete symmetries and torsion homology in F-theory journal, June 2015

Complete intersection fibers in F-theory journal, March 2015

F-theory vacua with Z 3 gauge symmetry journal, September 2015

Yukawas and discrete symmetries in F-theory compactifications without section journal, November 2014

Evidence for F-theory journal, June 1996

Heterotic string/F-theory duality from mirror symmetry journal, January 1998

Compactifications of F-theory on Calabi-Yau threefolds. (I) journal, August 1996

Physics of F-theory compactifications without section journal, December 2014

Triples, fluxes, and strings journal, January 2000

High U(1) charges in type IIB models and their F-theory lift journal, April 2019

Non-vanishing Heterotic Superpotentials on Elliptic Fibrations text, January 2018

Nongeometric heterotic strings and dual F-theory with enhanced gauge groups text, January 2018

High U(1) charges in type IIB models and their F-theory lift preprint, January 2018

Weierstrass models of elliptic toric $K3$ hypersurfaces and symplectic cuts
journal, January 2013

Mirror symmetry for lattice polarizedK3 surfaces
journal, September 1996

Refined stable pair invariants for E-, M- and [p, q]-strings
journal, November 2013

General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure
journal, November 2015

F-theory with quantized fluxes
journal, January 1999

Non-simply-connected gauge groups and rational points on elliptic curves
journal, July 1998

Prepotentials from symmetric products
journal, January 1999

Quartic gauge couplings from $K3$ geometry
journal, January 1999

Vector Bundles and F Theory
journal, August 1997

Aspects of the hypermultiplet moduli space in string duality
journal, April 1998

Loop-corrected compactifications of the heterotic string with line bundles
journal, June 2005

Picard Group of Hypersurfaces in Toric 3-Folds
journal, February 2012

Discrete gauge symmetries by Higgsing in four-dimensional F-theory compactifications
journal, December 2014

Elliptic fibrations with rank three Mordell-Weil group: F-theory with U(1)×U(1)×U(1) gauge symmetry
journal, March 2014

Prepotential, mirror map and $F$-theory on $K3$
journal, January 1998

Complete classification of reflexive polyhedra in four dimensions
journal, January 2000

On type IIB vacua with varying coupling constant
journal, October 1999

F-theory on all toric hypersurface fibrations and its Higgs branches
journal, January 2015

Compactifications of F-theory on Calabi-Yau threefolds (II)
journal, September 1996

Mordell-Weil torsion in the mirror of multi-sections
journal, December 2016

F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds
journal, October 2012

F-theory on genus-one fibrations
journal, August 2014

F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections
journal, June 2013

Geometric singularities and enhanced gauge symmetries
journal, December 1996

On discrete symmetries and torsion homology in F-theory
journal, June 2015

Complete intersection fibers in F-theory
journal, March 2015

F-theory vacua with $Z_{3}$ gauge symmetry
journal, September 2015

Yukawas and discrete symmetries in F-theory compactifications without section
journal, November 2014

Evidence for F-theory
journal, June 1996

Heterotic string/F-theory duality from mirror symmetry
journal, January 1998

Compactifications of F-theory on Calabi-Yau threefolds. (I)
journal, August 1996

Physics of F-theory compactifications without section
journal, December 2014

Triples, fluxes, and strings
journal, January 2000

High U(1) charges in type IIB models and their F-theory lift
journal, April 2019

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Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
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