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Title: General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure

Abstract

We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)×U(1) gauge symmetry. Generic U(1)×U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)×SU(2)×SU(3), SU(2)3×SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. In conclusion, the construction suggests a generalization to U(1) k factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups.

Authors:
 [1];  [2];  [3];  [4]
  1. Univ. of Pennsylvania, Philadelphia, PA (United States); Univ. of Maribor, Maribor (Slovenia)
  2. European Organization for Nuclear Research (CERN), Geneva (Switzerland)
  3. Univ. of Pennsylvania, Philadelphia, PA (United States)
  4. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1436880
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: 2015; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; F-Theory; Differential and Algebraic Geometry; Gauge Symmetry

Citation Formats

Cvetic, Mirjam, Klevers, Denis, Piragua, Hernan, and Taylor, Washington. General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure. United States: N. p., 2015. Web. doi:10.1007/JHEP11(2015)204.
Cvetic, Mirjam, Klevers, Denis, Piragua, Hernan, & Taylor, Washington. General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure. United States. doi:10.1007/JHEP11(2015)204.
Cvetic, Mirjam, Klevers, Denis, Piragua, Hernan, and Taylor, Washington. Mon . "General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure". United States. doi:10.1007/JHEP11(2015)204. https://www.osti.gov/servlets/purl/1436880.
@article{osti_1436880,
title = {General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure},
author = {Cvetic, Mirjam and Klevers, Denis and Piragua, Hernan and Taylor, Washington},
abstractNote = {We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)×U(1) gauge symmetry. Generic U(1)×U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)×SU(2)×SU(3), SU(2)3×SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. In conclusion, the construction suggests a generalization to U(1) k factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups.},
doi = {10.1007/JHEP11(2015)204},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2015,
place = {United States},
year = {2015},
month = {11}
}

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Cited by: 26 works
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Figures / Tables:

Figure 1 Figure 1: Weight lattice of charges in a theory with a U(1)×U(1) gauge group realized by Higgsing a theory with gauge group SU(2)×SU(2). Dots in red indicate the adjoint, dots in blue the bifundamental and black dots are the fundamentals. The origin is indicated by an extra circle.

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Works referenced in this record:

New branches of string compactifications and their F-theory duals
journal, May 1997


Compact F-theory GUTs with U(1)PQ
journal, April 2010

  • Marsano, Joseph; Saulina, Natalia; Schäfer-Nameki, Sakura
  • Journal of High Energy Physics, Vol. 2010, Issue 4
  • DOI: 10.1007/JHEP04(2010)095

Three-family particle physics models from global F-theory compactifications
journal, August 2015

  • Cvetič, Mirjam; Klevers, Denis; Peña, Damián Kaloni Mayorga
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)087

U(1) symmetries in F-theory GUTs with multiple sections
journal, March 2013

  • Mayrhofer, Christoph; Palti, Eran; Weigand, Timo
  • Journal of High Energy Physics, Vol. 2013, Issue 3
  • DOI: 10.1007/JHEP03(2013)098

Froggatt-Nielsen meets Mordell-Weil: a phenomenological survey of global F-theory GUTs with U(1)s
journal, November 2015

  • Krippendorf, Sven; Schäfer-Nameki, Sakura; Wong, Jin-Mann
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)008

Constraints on 6D supergravity theories with abelian gauge symmetry
journal, January 2012

  • Park, Daniel S.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2012, Issue 1
  • DOI: 10.1007/JHEP01(2012)141

Gauge fluxes in F-theory and type IIB orientifolds
journal, August 2012

  • Krause, Sven; Mayrhofer, Christoph; Weigand, Timo
  • Journal of High Energy Physics, Vol. 2012, Issue 8
  • DOI: 10.1007/JHEP08(2012)119

Charge lattices and consistency of 6D supergravity
journal, June 2011

  • Seiberg, Nathan; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2011, Issue 6
  • DOI: 10.1007/JHEP06(2011)001

Matter and singularities
journal, January 2012

  • Morrison, David R.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2012, Issue 1
  • DOI: 10.1007/JHEP01(2012)022

F-theory compactifications with multiple U(1)-factors: addendum
journal, December 2013

  • Cvetič, Mirjam; Klevers, Denis; Piragua, Hernan
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)056

Breaking GUT groups in F-theory
journal, January 2011


F-theory and all things rational: surveying U(1) symmetries with rational sections
journal, September 2015

  • Lawrie, Craig; Schäfer-Nameki, Sakura; Wong, Jin-Mann
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)144

Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections
journal, May 2005


F-theory compactifications for supersymmetric GUTs
journal, August 2009

  • Marsano, Joseph; Saulina, Natalia; Schäfer-Nameki, Sakura
  • Journal of High Energy Physics, Vol. 2009, Issue 08
  • DOI: 10.1088/1126-6708/2009/08/030

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

  • Cvetič, Mirjam; Klevers, Denis; Piragua, Hernan
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)021

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

  • Klevers, Denis; Mayorga Peña, Damián Kaloni; Oehlmann, Paul-Konstantin
  • Journal of High Energy Physics, Vol. 2015, Issue 1
  • DOI: 10.1007/JHEP01(2015)142

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


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

  • Morrison, David R.; Park, Daniel S.
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)128

String universality in six dimensions
journal, January 2011


Global F-theory GUTs
journal, April 2010


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

  • Cvetič, Mirjam; Klevers, Denis; Piragua, Hernan
  • Journal of High Energy Physics, Vol. 2013, Issue 6
  • DOI: 10.1007/JHEP06(2013)067

Anomaly-free chiral theories in six dimensions
journal, January 1985


Model building with $F$-theory
journal, January 2011


On hypercharge flux and exotics in F-theory GUTs
journal, September 2010


Non-Higgsable clusters for 4D F-theory models
journal, May 2015

  • Morrison, David R.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)080

Anomalies and the Euler characteristic of elliptic Calabi–Yau threefolds
journal, January 2012

  • Grassi, Antonella; Morrison, David R.
  • Communications in Number Theory and Physics, Vol. 6, Issue 1
  • DOI: 10.4310/CNTP.2012.v6.n1.a2

Evidence for F-theory
journal, June 1996


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


Small resolutions of SU(5)-models in F-theory
journal, January 2013


GUTs and exceptional branes in F-theory — I
journal, January 2009


Anomaly cancellation in six dimensions
journal, April 1994

  • Erler, Jens
  • Journal of Mathematical Physics, Vol. 35, Issue 4
  • DOI: 10.1063/1.530885

Geometric engineering in toric F-theory and GUTs with U(1) gauge factors
journal, December 2013

  • Braun, Volker; Grimm, Thomas W.; Keitel, Jan
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)069

Chiral four-dimensional F-theory compactifications with SU(5) and multiple U(1)-factors
journal, April 2014

  • Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis
  • Journal of High Energy Physics, Vol. 2014, Issue 4
  • DOI: 10.1007/JHEP04(2014)010

A note on the Green-Schwarz mechanism in open-string theories
journal, November 1992


6D supergravity without tensor multiplets
journal, April 2011

  • Kumar, Vijay; Park, Daniel S.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2011, Issue 4
  • DOI: 10.1007/JHEP04(2011)080

Yukawas, G-flux, and spectral covers from resolved Calabi-Yau’s
journal, November 2011

  • Marsano, Joseph; Schäfer-Nameki, Sakura
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)098

F-theory GUT vacua on compact Calabi-Yau fourfolds
journal, July 2010

  • Grimm, Thomas W.; Krause, Sven; Weigand, Timo
  • Journal of High Energy Physics, Vol. 2010, Issue 7
  • DOI: 10.1007/JHEP07(2010)037

Tate’s algorithm and F-theory
journal, August 2011

  • Katz, Sheldon; Morrison, David R.; Schäfer-Nameki, Sakura
  • Journal of High Energy Physics, Vol. 2011, Issue 8
  • DOI: 10.1007/JHEP08(2011)094

Mapping 6D $ \mathcal{N} = 1 $ supergravities to F-theory
journal, February 2010

  • Kumar, Vijay; Morrison, David R.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2010, Issue 2
  • DOI: 10.1007/JHEP02(2010)099

Rational F-theory GUTs without exotics
journal, July 2014

  • Krippendorf, Sven; Peña, Damián Kaloni Mayorga; Oehlmann, Paul-Konstantin
  • Journal of High Energy Physics, Vol. 2014, Issue 7
  • DOI: 10.1007/JHEP07(2014)013

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journal, May 2014


Generalized Green-Schwarz mechanism in F theory
journal, November 1996


ℙ 1 $$ {\mathrm{\mathbb{P}}}^1 $$ -bundle bases and the prevalence of non-Higgsable structure in 4D F-theory models
journal, September 2015

  • Halverson, James; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)086

Global aspects of the space of 6D $ \mathcal{N} = 1 $ supergravities
journal, November 2010

  • Kumar, Vijay; Morrison, David R.; Taylor, Washington
  • Journal of High Energy Physics, Vol. 2010, Issue 11
  • DOI: 10.1007/JHEP11(2010)118

Anomaly equations and intersection theory
journal, January 2012


Towards the Standard Model in F-theory: Towards the Standard Model in F-theory
journal, January 2015


-flux, chiral matter and singularity resolution in F-theory compactifications
journal, May 2012


Geometric singularities and enhanced gauge symmetries
journal, December 1996


Complete intersection fibers in F-theory
journal, March 2015

  • Braun, Volker; Grimm, Thomas W.; Keitel, Jan
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/JHEP03(2015)125

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


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

  • Anderson, Lara B.; García-Etxebarria, Iñaki; Grimm, Thomas W.
  • Journal of High Energy Physics, Vol. 2014, Issue 12
  • DOI: 10.1007/JHEP12(2014)156