Towards exotic matter and discrete non-abelian symmetries in F-theory

Cvetič, Mirjam; Heckman, Jonathan J.; Lin, Ling

doi:10.1007/jhep11(2018)001

Title: Towards exotic matter and discrete non-abelian symmetries in F-theory

Abstract

We present a prescription in F-theory for realizing matter in “exotic” representations of product gauge groups. For 6D vacua, bifundamental hypermultiplets are engineered by starting at a singular point in moduli space which includes 6D superconformal field theories coupled to gravity. A deformation in Higgs branch moduli space takes us to a weakly coupled gauge theory description. In the corresponding elliptically fibered Calabi-Yau threefold, the minimal Weierstrass model parameters (ƒ, g, Δ) vanish at collisions of the discriminant at least to order (4, 6, 12), but with sufficiently high order of tangency to ensure the existence of T-brane deformations to a weakly coupled gauge theory with exotic bifundamentals. We present explicit examples including bifundamental hypermultiplets of e₇ × su₂ and e₆ × su₃, each of which have dual heterotic orbifold descriptions. Geometrically, these matter fields are delocalized across multiple points of an F-theory geometry. Symmetry breaking with such representations can be used to produce high dimension representations of simple gauge groups such as the four-index symmetric representation of su₂ and the three-index symmetric representation of su₃, and after further higgsing can yield discrete non-abelian symmetries.

Authors:

Cvetič, Mirjam ^[1]; Heckman, Jonathan J. ^[2]; Lin, Ling ^[2]

Univ. of Pennsylvania, Philadelphia, PA (United States); Univ. of Maribor (Slovenia)
Univ. of Pennsylvania, Philadelphia, PA (United States)

Publication Date:: 2018-11-05

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

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1612002

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: 2018; 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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; F-Theory; String Duality; Superstrings and Heterotic Strings

Citation Formats


                    Cvetič, Mirjam, Heckman, Jonathan J., and Lin, Ling. Towards exotic matter and discrete non-abelian symmetries in F-theory.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep11(2018)001.

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                    Cvetič, Mirjam, Heckman, Jonathan J., & Lin, Ling. Towards exotic matter and discrete non-abelian symmetries in F-theory.  United States.  https://doi.org/10.1007/jhep11(2018)001

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                    Cvetič, Mirjam, Heckman, Jonathan J., and Lin, Ling. Mon .  
"Towards exotic matter and discrete non-abelian symmetries in F-theory".  United States.  https://doi.org/10.1007/jhep11(2018)001.  https://www.osti.gov/servlets/purl/1612002.

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@article{osti_1612002,

  title        = {Towards exotic matter and discrete non-abelian symmetries in F-theory},

  author       = {Cvetič, Mirjam and Heckman, Jonathan J. and Lin, Ling},

  abstractNote = {We present a prescription in F-theory for realizing matter in “exotic” representations of product gauge groups. For 6D vacua, bifundamental hypermultiplets are engineered by starting at a singular point in moduli space which includes 6D superconformal field theories coupled to gravity. A deformation in Higgs branch moduli space takes us to a weakly coupled gauge theory description. In the corresponding elliptically fibered Calabi-Yau threefold, the minimal Weierstrass model parameters (ƒ, g, Δ) vanish at collisions of the discriminant at least to order (4, 6, 12), but with sufficiently high order of tangency to ensure the existence of T-brane deformations to a weakly coupled gauge theory with exotic bifundamentals. We present explicit examples including bifundamental hypermultiplets of e7 × su2 and e6 × su3, each of which have dual heterotic orbifold descriptions. Geometrically, these matter fields are delocalized across multiple points of an F-theory geometry. Symmetry breaking with such representations can be used to produce high dimension representations of simple gauge groups such as the four-index symmetric representation of su2 and the three-index symmetric representation of su3, and after further higgsing can yield discrete non-abelian symmetries.},

  doi          = {10.1007/jhep11(2018)001},

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

  number       = 11,

  volume       = 2018,

  place        = {United States},

  year         = {2018},

  month        = {11}

}

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Title: Towards exotic matter and discrete non-abelian symmetries in F-theory

Abstract

Citation Formats

String theory and the path to unification: A review of recent developments journal, August 1997

Strings on orbifolds journal, January 1985

LieART—A Mathematica application for Lie algebras and representation theory journal, July 2015

T-branes and geometry journal, May 2014

On the geometry of the string landscape and the swampland journal, March 2007

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

T-branes and monodromy journal, July 2011

T-branes and matrix models journal, June 2017

F-theory on singular spaces journal, September 2015

T-branes at the limits of geometry journal, October 2017

Non-Abelian discrete gauge symmetries in F-theory journal, February 2016

Anomaly cancellation and abelian gauge symmetries in F-theory journal, February 2013

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

Matter from geometry journal, July 1997

Exotic matter on singular divisors in F-theory journal, November 2017

Weierstrass meets Enriques journal, February 2010

The heterotic string, the tangent bundle and derived categories journal, January 1998

T-branes as branes within branes journal, September 2015

Compact T-branes journal, September 2017

Non-Abelian discrete groups from the breaking of continuous flavor symmetries journal, September 2009

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

More on the matter of 6D SCFTs journal, July 2015

Dibaryons, branes, and strings in AdS orbifold models journal, December 1998

There and back again: a T-brane’s tale journal, November 2016

Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries journal, July 2017

Strings on orbifolds (II) journal, September 1986

Abelian F-theory models with charge-3 and charge-4 matter journal, May 2018

Evidence for F-theory journal, June 1996

Origin of family symmetries journal, October 2012

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

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

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

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

The global gauge group structure of F-theory compactification with U(1)s journal, January 2018

An infinite swampland of U(1) charge spectra in 6D supergravity theories journal, June 2018

Stringy origin of non-Abelian discrete flavor symmetries journal, April 2007

Non-Abelian discrete gauge symmetries in 4d string models journal, September 2012

Z p charged branes in flux compactifications journal, April 2013

Simple Non-Abelian Finite Flavor Groups and Fermion Masses journal, December 1995

Merging heterotic orbifolds and K3 compactifications with line bundles journal, January 2007

F-theory duals of singular heterotic K3 models journal, January 2015

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

Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models journal, June 2016

Colliding singularities in F-theory and phase transitions journal, March 1997

Point-like instantons on K3 orbifolds journal, October 1997

On the classification of 6D SCFTs and generalized ADE orbifolds journal, May 2014

6D SCFTs and gravity journal, June 2015

F-theory on quotient threefolds with (2,0) discrete superconformal matter journal, June 2018

T-branes and α ′ -corrections journal, November 2016

6d Conformal matter journal, February 2015

Atomic classification of 6D SCFTs: Atomic classification of 6D SCFTs journal, June 2015

Spontaneous breaking of SU(3) to finite family symmetries — a pedestrian’s approach journal, March 2011

Geometric singularities and enhanced gauge symmetries journal, December 1996

Classifying bases for 6D F-theory models journal, January 2012

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

F-theory and N $$ \mathcal{N} $$ = 1 SCFTs in four dimensions journal, August 2016

4D gauge theories with conformal matter journal, September 2018

F-theory at constant coupling journal, September 1996

Abelian gauge symmetries and proton decay in global F -theory GUTs journal, October 2010

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

More on the Matter of 6D SCFTs preprint, January 2014

The Heterotic String, the Tangent Bundle, and Derived Categories text, January 1998

Nilpotent networks and 4D RG flows journal, May 2019

T-branes and G 2 backgrounds journal, January 2020

The two faces of T-branes journal, October 2019

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

Fission, Fusion, and 6D RG Flows text, January 2018

Nilpotent Networks and 4D RG Flows text, January 2018

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

The two faces of T-branes text, January 2019

String theory and the path to unification: A review of recent developments
journal, August 1997

Strings on orbifolds
journal, January 1985

LieART—A Mathematica application for Lie algebras and representation theory
journal, July 2015

T-branes and geometry
journal, May 2014

On the geometry of the string landscape and the swampland
journal, March 2007

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

T-branes and monodromy
journal, July 2011

T-branes and matrix models
journal, June 2017

F-theory on singular spaces
journal, September 2015

T-branes at the limits of geometry
journal, October 2017

Non-Abelian discrete gauge symmetries in F-theory
journal, February 2016

Anomaly cancellation and abelian gauge symmetries in F-theory
journal, February 2013

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

Matter from geometry
journal, July 1997

Exotic matter on singular divisors in F-theory
journal, November 2017

Weierstrass meets Enriques
journal, February 2010

The heterotic string, the tangent bundle and derived categories
journal, January 1998

T-branes as branes within branes
journal, September 2015

Compact T-branes
journal, September 2017

Non-Abelian discrete groups from the breaking of continuous flavor symmetries
journal, September 2009

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

More on the matter of 6D SCFTs
journal, July 2015

Dibaryons, branes, and strings in AdS orbifold models
journal, December 1998

There and back again: a T-brane’s tale
journal, November 2016

Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries
journal, July 2017

Strings on orbifolds (II)
journal, September 1986

Abelian F-theory models with charge-3 and charge-4 matter
journal, May 2018

Evidence for F-theory
journal, June 1996

Origin of family symmetries
journal, October 2012

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

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

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

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

The global gauge group structure of F-theory compactification with U(1)s
journal, January 2018

An infinite swampland of U(1) charge spectra in 6D supergravity theories
journal, June 2018

Stringy origin of non-Abelian discrete flavor symmetries
journal, April 2007

Non-Abelian discrete gauge symmetries in 4d string models
journal, September 2012

Z p charged branes in flux compactifications
journal, April 2013

Simple Non-Abelian Finite Flavor Groups and Fermion Masses
journal, December 1995

Merging heterotic orbifolds and K3 compactifications with line bundles
journal, January 2007

F-theory duals of singular heterotic K3 models
journal, January 2015

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

Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models
journal, June 2016

Colliding singularities in F-theory and phase transitions
journal, March 1997

Point-like instantons on K3 orbifolds
journal, October 1997

On the classification of 6D SCFTs and generalized ADE orbifolds
journal, May 2014

6D SCFTs and gravity
journal, June 2015

F-theory on quotient threefolds with (2,0) discrete superconformal matter
journal, June 2018

T-branes and α ′ -corrections
journal, November 2016

6d Conformal matter
journal, February 2015

Atomic classification of 6D SCFTs: Atomic classification of 6D SCFTs
journal, June 2015

Spontaneous breaking of SU(3) to finite family symmetries — a pedestrian’s approach
journal, March 2011

Geometric singularities and enhanced gauge symmetries
journal, December 1996

Classifying bases for 6D F-theory models
journal, January 2012

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

F-theory and N $$ \mathcal{N} $$ = 1 SCFTs in four dimensions
journal, August 2016

4D gauge theories with conformal matter
journal, September 2018

F-theory at constant coupling
journal, September 1996

Abelian gauge symmetries and proton decay in global $F$ -theory GUTs
journal, October 2010

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

More on the Matter of 6D SCFTs
preprint, January 2014

The Heterotic String, the Tangent Bundle, and Derived Categories
text, January 1998

Nilpotent networks and 4D RG flows
journal, May 2019

T-branes and $G_{2}$ backgrounds
journal, January 2020

The two faces of T-branes
journal, October 2019

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

Fission, Fusion, and 6D RG Flows
text, January 2018

Nilpotent Networks and 4D RG Flows
text, January 2018

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

The two faces of T-branes
text, January 2019