Reflections on the matter of 3D N = 1 vacua and local S p i n ( 7 ) compactifications

Cvetič, Mirjam; Heckman, Jonathan J.; Torres, Ethan; Zoccarato, Gianluca

doi:10.1103/PhysRevD.105.026008

Title: Reflections on the matter of 3D $N = 1$ vacua and local $S p i n (7)$ compactifications

Abstract

We use Higgs bundles to study the 3D $$\mathscr{N}$$ = 1 vacua obtained from M-theory compactified on a local Spin(7) space given as a four-manifold M₄ of ADE singularities with further generic enhancements in the singularity type along one-dimensional subspaces. There can be strong quantum corrections to the massless degrees of freedom in the low energy effective field theory, but topologically robust quantities such as “parity” anomalies are still calculable. We show how geometric reflections of the compactification space descend to 3D reflections and discrete symmetries. The parity anomalies of the effective field theory descend from topological data of the compactification. The geometric perspective also allows us to track various perturbative and nonperturbative corrections to the 3D effective field theory. We also provide some explicit constructions of well-known 3D theories, including those which arise as edge modes of 4D topological insulators, and 3D $$\mathscr{N}$$ = 1 analogs of grand unified theories. An additional result of our analysis is that we are able to track the spectrum of extended objects and their transformations under higher-form symmetries.

Authors:

Cvetič, Mirjam; Heckman, Jonathan J.;

; Zoccarato, Gianluca

Publication Date:: Fri Jan 07 00:00:00 EST 2022

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

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation; Fay R. and Eugene L. Langberg Endowment; Slovenian Research Agency; University of Pennsylvania

OSTI Identifier:: 1838892

Alternate Identifier(s):: OSTI ID: 1980012

Grant/Contract Number:: SC0013528; SC0021484; 724069; P1-0306

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 105 Journal Issue: 2; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; compactification; geometry; M-theory; quantum field theory; string theory techniques in condensed matter; strings and branes; supersymmetry; topology

Citation Formats


                    Cvetič, Mirjam, Heckman, Jonathan J., Torres, Ethan, and Zoccarato, Gianluca. Reflections on the matter of 3D N = 1 vacua and local S p i n ( 7 ) compactifications.  United States: N. p., 2022. 
Web.  doi:10.1103/PhysRevD.105.026008.

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                    Cvetič, Mirjam, Heckman, Jonathan J., Torres, Ethan, & Zoccarato, Gianluca. Reflections on the matter of 3D N = 1 vacua and local S p i n ( 7 ) compactifications.  United States.  https://doi.org/10.1103/PhysRevD.105.026008

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                    Cvetič, Mirjam, Heckman, Jonathan J., Torres, Ethan, and Zoccarato, Gianluca. Fri .  
"Reflections on the matter of 3D N = 1 vacua and local S p i n ( 7 ) compactifications".  United States.  https://doi.org/10.1103/PhysRevD.105.026008.

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@article{osti_1838892,

  title        = {Reflections on the matter of 3D N = 1 vacua and local S p i n ( 7 ) compactifications},

  author       = {Cvetič, Mirjam and Heckman, Jonathan J. and Torres, Ethan and Zoccarato, Gianluca},

  abstractNote = {We use Higgs bundles to study the 3D $\mathscr{N}$ = 1 vacua obtained from M-theory compactified on a local Spin(7) space given as a four-manifold M4 of ADE singularities with further generic enhancements in the singularity type along one-dimensional subspaces. There can be strong quantum corrections to the massless degrees of freedom in the low energy effective field theory, but topologically robust quantities such as “parity” anomalies are still calculable. We show how geometric reflections of the compactification space descend to 3D reflections and discrete symmetries. The parity anomalies of the effective field theory descend from topological data of the compactification. The geometric perspective also allows us to track various perturbative and nonperturbative corrections to the 3D effective field theory. We also provide some explicit constructions of well-known 3D theories, including those which arise as edge modes of 4D topological insulators, and 3D $\mathscr{N}$ = 1 analogs of grand unified theories. An additional result of our analysis is that we are able to track the spectrum of extended objects and their transformations under higher-form symmetries.},

  doi          = {10.1103/PhysRevD.105.026008},

  journal      = {Physical Review D},

  number       = 2,

  volume       = 105,

  place        = {United States},

  year         = {Fri Jan 07 00:00:00 EST 2022},

  month        = {Fri Jan 07 00:00:00 EST 2022}

}

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Title: Reflections on the matter of 3D N = 1 vacua and local S p i n ( 7 ) compactifications

Abstract

Citation Formats

Cobordism conjecture, anomalies, and the String Lamppost Principle journal, January 2021

Higher form symmetries and M-theory journal, December 2020

Why are fractional charges of orientifolds compatible with Dirac quantization? journal, January 2019

The “parity” anomaly on an unorientable manifold journal, November 2016

Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions journal, February 2016

New complete noncompact Spin(7) manifolds journal, January 2002

Five-brane effective action in M-theory journal, May 1997

Matter from geometry journal, July 1997

Geometric approach to 3D interfaces at strong coupling journal, November 2020

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Coulomb and Higgs branches from canonical singularities. Part 0 journal, February 2021

Time reversal, S U ( N ) Yang–Mills and cobordisms: Interacting topological superconductors/insulators and quantum spin liquids in 3 + 1 D journal, July 2018

Up-type quark masses in SU(5) F-theory models journal, November 2013

Time-reversal symmetry, anomalies, and dualities in (2+1)$d$ journal, January 2018

The partition bundle of type A N−1 (2, 0) theory journal, April 2011

Zero-sets of near-sympletic forms journal, January 2006

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

Dai-Freed anomalies in particle physics journal, August 2019

Frozen singularities in M and F theory journal, June 2016

Evidence for F-theory journal, June 1996

Gapped boundary phases of topological insulators via weak coupling journal, November 2016

Chiral anomalies on a circle and their cancellation in F-theory journal, April 2018

GUTs and exceptional branes in F-theory — II. Experimental predictions journal, January 2009

d -Brane Instantons in Type II Orientifolds journal, November 2009

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

Flavor hierarchy from F-theory journal, September 2010

A note on compactifications on spin(7)-holonomy manifolds journal, May 2001

Higher-form symmetries in 5d journal, September 2020

Supergravity in theory in 11 dimensions journal, June 1978

Anti-de Sitter space and the center of the gauge group journal, November 1998

On a Theorem of Torelli journal, October 1958

Quantum Spin Hall Effect in Graphene journal, November 2005

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

On flux quantization in M-theory and the effective action journal, April 1997

F-theory and neutrinos: Kaluza-Klein dilution of flavor hierarchy journal, January 2010

A strong coupling test of S-duality journal, December 1994

Is Supersymmetry Really Broken? journal, March 1995

Toroidal compactification without vector structure journal, February 1998

Omega vs. pi, and 6d anomaly cancellation journal, May 2021

4D gauge theories with conformal matter journal, September 2018

Non-perturbative effects and Yukawa hierarchies in F-theory SU(5) unification journal, March 2013

The quotient space of the complex projective plane under conjugation is a 4-sphere journal, December 1973

Non-perturbative superpotentials in string theory journal, August 1996

Corrigendum to “More on the matter of 6D SCFTs” [Phys. Lett. B 747 (2015) 73–75] journal, September 2020

Yukawa hierarchies in global F-theory models journal, January 2020

Higher-form symmetries and their anomalies in M-/F-theory duality journal, December 2021

Nonperturbative Effects on Seven-Brane Yukawa Couplings journal, June 2010

Yukawa hierarchies at the point of E8 in F-theory journal, April 2015

CFT's from Calabi–Yau four-folds journal, September 2000

Higher anomalies, higher symmetries, and cobordisms I: classification of higher-symmetry-protected topological states and their boundary fermionic/bosonic anomalies via a generalized cobordism theory journal, January 2019

Higher-form symmetries of 6d and 5d theories journal, February 2021

Topological field theories on manifolds with Wu structures journal, April 2017

Topological insulators and superconductors journal, October 2011

Supersymmetry and Morse theory journal, January 1982

Cohomogeneity one manifolds of Spin(7) and G 2 holonomy journal, May 2002

Higgs bundles for M-theory on G2-manifolds journal, March 2019

Baryons, monopoles and dualities in Chern-Simons-matter theories journal, February 2016

Anomalies and fermion zero modes on strings and domain walls journal, January 1985

Conifold transitions and five-brane condensation in M-theory on Spin (7) manifolds journal, January 2003

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Supersymmetry, G-flux and Spin(7) manifolds journal, September 2002

Pixelated Dark Energy journal, August 2019

Heisenberg groups and noncommutative fluxes journal, January 2007

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6d Conformal matter journal, February 2015

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Generalized global symmetries journal, February 2015

Erratum: non-perturbative effects and Yukawa hierarchies in F-theory SU(5) unification journal, July 2013

Fermion path integrals and topological phases journal, July 2016

Erratum: “η-invariants and determinant lines” [J. Math. Phys. 35, 5155 (1994)] journal, January 2001

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Title: Reflections on the matter of 3D $N = 1$ vacua and local $S p i n (7)$ compactifications

Cobordism conjecture, anomalies, and the String Lamppost Principle
journal, January 2021

Higher form symmetries and M-theory
journal, December 2020

Why are fractional charges of orientifolds compatible with Dirac quantization?
journal, January 2019

The “parity” anomaly on an unorientable manifold
journal, November 2016

Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
journal, February 2016

New complete noncompact Spin(7) manifolds
journal, January 2002

Five-brane effective action in M-theory
journal, May 1997

Matter from geometry
journal, July 1997

Geometric approach to 3D interfaces at strong coupling
journal, November 2020

Geometric unification of Higgs bundle vacua
journal, November 2020

Coulomb and Higgs branches from canonical singularities. Part 0
journal, February 2021

Time reversal, $S U (N)$ Yang–Mills and cobordisms: Interacting topological superconductors/insulators and quantum spin liquids in $3 + 1 D$
journal, July 2018

Up-type quark masses in SU(5) F-theory models
journal, November 2013

Time-reversal symmetry, anomalies, and dualities in (2+1)$d$
journal, January 2018

The partition bundle of type A N−1 (2, 0) theory
journal, April 2011

Zero-sets of near-sympletic forms
journal, January 2006

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

Dai-Freed anomalies in particle physics
journal, August 2019

Frozen singularities in M and F theory
journal, June 2016

Evidence for F-theory
journal, June 1996

Gapped boundary phases of topological insulators via weak coupling
journal, November 2016

Chiral anomalies on a circle and their cancellation in F-theory
journal, April 2018

GUTs and exceptional branes in F-theory — II. Experimental predictions
journal, January 2009

d -Brane Instantons in Type II Orientifolds
journal, November 2009

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

Flavor hierarchy from F-theory
journal, September 2010

A note on compactifications on spin(7)-holonomy manifolds
journal, May 2001

Higher-form symmetries in 5d
journal, September 2020

Supergravity in theory in 11 dimensions
journal, June 1978

Anti-de Sitter space and the center of the gauge group
journal, November 1998

On a Theorem of Torelli
journal, October 1958

Quantum Spin Hall Effect in Graphene
journal, November 2005

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

On flux quantization in M-theory and the effective action
journal, April 1997

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journal, January 2010

A strong coupling test of S-duality
journal, December 1994

Is Supersymmetry Really Broken?
journal, March 1995

Toroidal compactification without vector structure
journal, February 1998

Omega vs. pi, and 6d anomaly cancellation
journal, May 2021

4D gauge theories with conformal matter
journal, September 2018

Non-perturbative effects and Yukawa hierarchies in F-theory SU(5) unification
journal, March 2013

The quotient space of the complex projective plane under conjugation is a 4-sphere
journal, December 1973

Non-perturbative superpotentials in string theory
journal, August 1996

Corrigendum to “More on the matter of 6D SCFTs” [Phys. Lett. B 747 (2015) 73–75]
journal, September 2020

Yukawa hierarchies in global F-theory models
journal, January 2020

Higher-form symmetries and their anomalies in M-/F-theory duality
journal, December 2021

Nonperturbative Effects on Seven-Brane Yukawa Couplings
journal, June 2010

Yukawa hierarchies at the point of E8 in F-theory
journal, April 2015

CFT's from Calabi–Yau four-folds
journal, September 2000

Higher anomalies, higher symmetries, and cobordisms I: classification of higher-symmetry-protected topological states and their boundary fermionic/bosonic anomalies via a generalized cobordism theory
journal, January 2019

Higher-form symmetries of 6d and 5d theories
journal, February 2021

Topological field theories on manifolds with Wu structures
journal, April 2017

Topological insulators and superconductors
journal, October 2011

Supersymmetry and Morse theory
journal, January 1982

Cohomogeneity one manifolds of Spin(7) and G 2 holonomy
journal, May 2002

Higgs bundles for M-theory on G2-manifolds
journal, March 2019

Baryons, monopoles and dualities in Chern-Simons-matter theories
journal, February 2016

Anomalies and fermion zero modes on strings and domain walls
journal, January 1985

Conifold transitions and five-brane condensation in M-theory on Spin (7) manifolds
journal, January 2003

Spin(7)-manifolds as generalized connected sums and 3d N = 1 $$ \mathcal{N}=1 $$ theories
journal, June 2018

Supersymmetry, G-flux and Spin(7) manifolds
journal, September 2002

Pixelated Dark Energy
journal, August 2019

Heisenberg groups and noncommutative fluxes
journal, January 2007

Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence
journal, January 2020

Characteristic Classes. (AM-76)
book, December 1974

6d Conformal matter
journal, February 2015

D-Brane probes of Special Holonomy Manifolds, and Dynamics of Script N = 1 Three-Dimensional Gauge Theories
journal, April 2002

Generalized global symmetries
journal, February 2015

Erratum: non-perturbative effects and Yukawa hierarchies in F-theory SU(5) unification
journal, July 2013

Fermion path integrals and topological phases
journal, July 2016

Erratum: “η-invariants and determinant lines” [J. Math. Phys. 35, 5155 (1994)]
journal, January 2001

F-theory on Spin(7) manifolds: weak-coupling limit
journal, February 2014

Local G2-manifolds, Higgs bundles and a colored quantum mechanics
journal, May 2021

The pin Groups in Physics: c, p and t
journal, August 2001

Curious aspects of three-dimensional N = 1 $$ \mathcal{N}=1 $$ SCFTs
journal, August 2018

Relative Quantum Field Theory
journal, January 2014

The global anomalies of (2,0) superconformal field theories in six dimensions
journal, September 2014

Anomaly polynomial of general 6D SCFTs
journal, October 2014

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