Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states

Apruzzi, Fabio; Lawrie, Craig; Lin, Ling; Schäfer-Nameki, Sakura; Wang, Yi-Nan

doi:10.1007/jhep11(2019)068

Title: Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states

Abstract

We propose a graph-based approach to 5d superconformal field theories (SCFTs) based on their realization as M-theory compactifications on singular elliptic Calabi–Yau threefolds. Fieldtheoretically, these 5d SCFTs descend from 6d N = (1, 0) SCFTs by circle compactification and mass deformations. We derive a description of these theories in terms of graphs, so-called Combined Fiber Diagrams, which encode salient features of the partially resolved Calabi–Yau geometry, and provides a combinatorial way of characterizing all 5d SCFTs that descend from a given 6d theory. Remarkably, these graphs manifestly capture strongly coupled data of the 5d SCFTs, such as the superconformal flavor symmetry, BPS states, and mass deformations. The capabilities of this approach are demonstrated by deriving all rank one and rank two 5d SCFTs. The full potential, however, becomes apparent when applied to theories with higher rank. Starting with the higher rank conformal matter theories in 6d, we are led to the discovery of previously unknown flavor symmetry enhancements and new 5d SCFTs.

Authors:

Apruzzi, Fabio ^[1]; Lawrie, Craig ^[2]; Lin, Ling ^[2]; Schäfer-Nameki, Sakura ^[1]; Wang, Yi-Nan ^[1]

Univ. of Oxford (United Kingdom). Mathematical Inst.
Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy

Publication Date:: Tue Nov 12 00:00:00 EST 2019

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

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

OSTI Identifier:: 1804014

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: 2019; Journal Issue: 11; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics

Citation Formats


                    Apruzzi, Fabio, Lawrie, Craig, Lin, Ling, Schäfer-Nameki, Sakura, and Wang, Yi-Nan. Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep11(2019)068.

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                    Apruzzi, Fabio, Lawrie, Craig, Lin, Ling, Schäfer-Nameki, Sakura, & Wang, Yi-Nan. Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states.  United States.  https://doi.org/10.1007/jhep11(2019)068

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                    Apruzzi, Fabio, Lawrie, Craig, Lin, Ling, Schäfer-Nameki, Sakura, and Wang, Yi-Nan. Tue .  
"Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states".  United States.  https://doi.org/10.1007/jhep11(2019)068.  https://www.osti.gov/servlets/purl/1804014.

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@article{osti_1804014,

  title        = {Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states},

  author       = {Apruzzi, Fabio and Lawrie, Craig and Lin, Ling and Schäfer-Nameki, Sakura and Wang, Yi-Nan},

  abstractNote = {We propose a graph-based approach to 5d superconformal field theories (SCFTs) based on their realization as M-theory compactifications on singular elliptic Calabi–Yau threefolds. Fieldtheoretically, these 5d SCFTs descend from 6d N = (1, 0) SCFTs by circle compactification and mass deformations. We derive a description of these theories in terms of graphs, so-called Combined Fiber Diagrams, which encode salient features of the partially resolved Calabi–Yau geometry, and provides a combinatorial way of characterizing all 5d SCFTs that descend from a given 6d theory. Remarkably, these graphs manifestly capture strongly coupled data of the 5d SCFTs, such as the superconformal flavor symmetry, BPS states, and mass deformations. The capabilities of this approach are demonstrated by deriving all rank one and rank two 5d SCFTs. The full potential, however, becomes apparent when applied to theories with higher rank. Starting with the higher rank conformal matter theories in 6d, we are led to the discovery of previously unknown flavor symmetry enhancements and new 5d SCFTs.},

  doi          = {10.1007/jhep11(2019)068},

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

  number       = 11,

  volume       = 2019,

  place        = {United States},

  year         = {Tue Nov 12 00:00:00 EST 2019},

  month        = {Tue Nov 12 00:00:00 EST 2019}

}

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6D SCFTs, center-flavor symmetries, and Stiefel-Whitney compactifications

Journal Article Heckman, Jonathan J. ; Lawrie, Craig ; Lin, Ling ; ... - Physical Review D

The center-flavor symmetry of a gauge theory specifies the global form of consistent gauge and flavor bundle background field configurations. For 6D gauge theories which arise from a tensor branch deformation of a superconformal field theory (SCFT), we determine the global structure of such background field configurations, including possible continuous Abelian symmetry and R-symmetry bundles. Proceeding to the conformal fixed point, this provides a prescription for reading off the global form of the continuous factors of the zero-form symmetry, including possible nontrivial mixing between flavor and R-symmetry. As an application, we show that this global structure leads to a largemore »« less
https://doi.org/10.1103/PhysRevD.106.066003
5d superconformal field theories and graphs

Journal Article Apruzzi, Fabio ; Lawrie, Craig ; Lin, Ling ; ... - Physics Letters B

We propose graphs, the Combined Fiber Diagrams (CFD), to characterize all 5d superconformal field theories (SCFTs) that arise as -reductions of 6d SCFTs. Transitions between CFDs encode mass deformations that trigger RG-flows between SCFTs. They provide a combinatorial classification of all such 5d SCFTs and encode physical information about the strongly coupled theories, like the superconformal flavor symmetry and BPS states. We consistently reproduce known results, but more importantly predict new theories and strong coupling effects in 5d SCFTs.
Cited by 69
https://doi.org/10.1016/j.physletb.2019.135077

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Title: Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states

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Citation Formats

Classification of 6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ gauge theories journal, November 2015

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

Branes, superpotentials and superconformal fixed points journal, October 1997

Euler Characteristics of Crepant Resolutions of Weierstrass Models journal, September 2019

Exploring 5d BPS Spectra with Exponential Networks journal, October 2019

Box graphs and singular fibers journal, May 2014

The Tate form on steroids: resolution and higher codimension fibers journal, April 2013

The frozen phase of F-theory journal, August 2018

Fibrations in CICY threefolds journal, October 2017

5-dim superconformal index with enhanced E n global symmetry journal, October 2012

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

Extremal transitions and five-dimensional supersymmetric field theories journal, January 1997

Tools for CICYs in F-theory journal, November 2016

Matter from geometry journal, July 1997

6d Conformal matter journal, February 2015

A note on non-flat points in the SU(5) × U(1)PQ F-theory model journal, May 2019

Discrete theta angle from an O5-plane journal, November 2017

Global Tensor-Matter Transitions in F-Theory journal, June 2018

General instanton counting and 5d SCFT journal, July 2015

Toric elliptic fibrations and F-theory compactifications journal, January 2013

The toric SO(10) F-theory landscape journal, December 2017

The Geometry of the SU(2) × G2-model journal, February 2019

On the global symmetries of 6D superconformal field theories journal, July 2016

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

Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective journal, January 2019

tt * geometry in 3 and 4 dimensions journal, May 2014

Geometric constraints on the space of N $$ \mathcal{N} $$ = 2 SCFTs. Part I: physical constraints on relevant deformations journal, February 2018

Codimension-three bundle singularities in F-theory journal, June 2002

Brane webs and O5-planes journal, March 2016

Five-branes, seven-branes and five-dimensional E n field theories journal, March 1999

Phase transitions in M-theory and F-theory journal, July 1996

Evidence for F-theory journal, June 1996

6D SCFTs and phases of 5D theories journal, September 2017

Phases of 5d SCFTs from M-/F-theory on non-flat fibrations journal, May 2019

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

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

5-brane webs, symmetry enhancement, and duality in 5d supersymmetric gauge theory journal, March 2014

Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers journal, February 2019

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

S 1 /T 2 compactifications of 6d N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ theories and brane webs journal, March 2016

E 8 instantons on type-A ALE spaces and supersymmetric field theories journal, September 2017

Fiber-base duality and global symmetry enhancement journal, April 2015

On geometric classification of 5d SCFTs journal, April 2018

M-theory on a Calabi-Yau manifold journal, May 1996

Brane webs, 5d gauge theories and 6d N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ SCFT’s journal, December 2015

On E 8 and F-theory GUTs journal, June 2015

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

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

Five dimensional SUSY field theories, non-trivial fixed points and string dynamics journal, November 1996

Box graphs and resolutions II: From Coulomb phases to fiber faces journal, April 2016

Box graphs and resolutions I journal, April 2016

Duality walls and defects in 5d N = 1 $$ \mathcal{N}=1 $$ theories journal, January 2017

Tropical geometry and five dimensional Higgs branches at infinite coupling journal, January 2019

Webs of ( p , q ) 5-branes, five dimensional field theories and grid diagrams journal, January 1998

5d fixed points from brane webs and O7-planes journal, December 2015

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

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

Three dimensional canonical singularity and five dimensional N $$ \mathcal{N} $$ = 1 SCFT journal, June 2017

5-brane webs for 5d $$ \mathcal{N} $$ = 1 G2 gauge theories journal, March 2018

Instanton operators and symmetry enhancement in 5D supersymmetric gauge theories journal, April 2015

Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces journal, July 1997

Classifying global symmetries of 6D SCFTs journal, March 2018

Anomaly equations and intersection theory journal, January 2012

A new 5d description of 6d D-type minimal conformal matter journal, August 2015

Branes, Calabi-Yau spaces, and toroidal compactification of the N = 1 six-dimensional E8 theory journal, March 1997

Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories journal, July 2015

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

Instanton operators and symmetry enhancement in 5d supersymmetric USp, SO and exceptional gauge theories journal, July 2015

Geometric singularities and enhanced gauge symmetries journal, December 1996

Non-toric bases for elliptic Calabi–Yau threefolds and 6D F-theory vacua journal, January 2017

A note on instanton operators, instanton particles, and supersymmetry journal, May 2016

Singular del Pezzo surfaces whose universal torsors are hypersurfaces journal, September 2013

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

11-Dimensional supergravity compactified on Calabi-Yau threefolds journal, August 1995

On S-duality of 5d super Yang-Mills on S 1 journal, November 2011

5d quivers and their AdS 6 duals journal, July 2012

The D4–D8 brane system and five dimensional fixed points journal, August 1999

Classification of 6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ gauge theories
journal, November 2015

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

Branes, superpotentials and superconformal fixed points
journal, October 1997

Euler Characteristics of Crepant Resolutions of Weierstrass Models
journal, September 2019

Exploring 5d BPS Spectra with Exponential Networks
journal, October 2019

Box graphs and singular fibers
journal, May 2014

The Tate form on steroids: resolution and higher codimension fibers
journal, April 2013

The frozen phase of F-theory
journal, August 2018

Fibrations in CICY threefolds
journal, October 2017

5-dim superconformal index with enhanced E n global symmetry
journal, October 2012

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

Extremal transitions and five-dimensional supersymmetric field theories
journal, January 1997

Tools for CICYs in F-theory
journal, November 2016

Matter from geometry
journal, July 1997

6d Conformal matter
journal, February 2015

A note on non-flat points in the SU(5) × U(1)PQ F-theory model
journal, May 2019

Discrete theta angle from an O5-plane
journal, November 2017

Global Tensor-Matter Transitions in F-Theory
journal, June 2018

General instanton counting and 5d SCFT
journal, July 2015

Toric elliptic fibrations and F-theory compactifications
journal, January 2013

The toric SO(10) F-theory landscape
journal, December 2017

The Geometry of the SU(2) × G2-model
journal, February 2019

On the global symmetries of 6D superconformal field theories
journal, July 2016

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

Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective
journal, January 2019

tt * geometry in 3 and 4 dimensions
journal, May 2014

Geometric constraints on the space of N $$ \mathcal{N} $$ = 2 SCFTs. Part I: physical constraints on relevant deformations
journal, February 2018

Codimension-three bundle singularities in F-theory
journal, June 2002

Brane webs and O5-planes
journal, March 2016

Five-branes, seven-branes and five-dimensional E _n field theories
journal, March 1999

Phase transitions in M-theory and F-theory
journal, July 1996

Evidence for F-theory
journal, June 1996

6D SCFTs and phases of 5D theories
journal, September 2017

Phases of 5d SCFTs from M-/F-theory on non-flat fibrations
journal, May 2019

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

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

5-brane webs, symmetry enhancement, and duality in 5d supersymmetric gauge theory
journal, March 2014

Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
journal, February 2019

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

S 1 /T 2 compactifications of 6d N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ theories and brane webs
journal, March 2016

E 8 instantons on type-A ALE spaces and supersymmetric field theories
journal, September 2017

Fiber-base duality and global symmetry enhancement
journal, April 2015

On geometric classification of 5d SCFTs
journal, April 2018

M-theory on a Calabi-Yau manifold
journal, May 1996

Brane webs, 5d gauge theories and 6d N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ SCFT’s
journal, December 2015

On E 8 and F-theory GUTs
journal, June 2015

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

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

Five dimensional SUSY field theories, non-trivial fixed points and string dynamics
journal, November 1996

Box graphs and resolutions II: From Coulomb phases to fiber faces
journal, April 2016

Box graphs and resolutions I
journal, April 2016

Duality walls and defects in 5d N = 1 $$ \mathcal{N}=1 $$ theories
journal, January 2017

Tropical geometry and five dimensional Higgs branches at infinite coupling
journal, January 2019

Webs of ( p , q ) 5-branes, five dimensional field theories and grid diagrams
journal, January 1998

5d fixed points from brane webs and O7-planes
journal, December 2015

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

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

Three dimensional canonical singularity and five dimensional N $$ \mathcal{N} $$ = 1 SCFT
journal, June 2017

5-brane webs for 5d $$ \mathcal{N} $$ = 1 G2 gauge theories
journal, March 2018

Instanton operators and symmetry enhancement in 5D supersymmetric gauge theories
journal, April 2015

Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces
journal, July 1997

Classifying global symmetries of 6D SCFTs
journal, March 2018

Anomaly equations and intersection theory
journal, January 2012

A new 5d description of 6d D-type minimal conformal matter
journal, August 2015

Branes, Calabi-Yau spaces, and toroidal compactification of the N = 1 six-dimensional E8 theory
journal, March 1997

Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories
journal, July 2015

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

Instanton operators and symmetry enhancement in 5d supersymmetric USp, SO and exceptional gauge theories
journal, July 2015

Geometric singularities and enhanced gauge symmetries
journal, December 1996

Non-toric bases for elliptic Calabi–Yau threefolds and 6D F-theory vacua
journal, January 2017

A note on instanton operators, instanton particles, and supersymmetry
journal, May 2016

Singular del Pezzo surfaces whose universal torsors are hypersurfaces
journal, September 2013

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

11-Dimensional supergravity compactified on Calabi-Yau threefolds
journal, August 1995

On S-duality of 5d super Yang-Mills on S 1
journal, November 2011

5d quivers and their AdS 6 duals
journal, July 2012

The D4–D8 brane system and five dimensional fixed points
journal, August 1999

Dualities and 5-brane webs for 5d rank 2 SCFTs
journal, December 2018

Low-energy analysis of M- and F-theories on Calabi-Yau threefolds
journal, August 1996

Global Tensor-Matter Transitions in F-Theory
journal, June 2018