The long flow to freedom

Aharony, Ofer; Razamat, Shlomo S.; Seiberg, Nathan; Willett, Brian

doi:10.1007/JHEP02(2017)056

Title: The long flow to freedom

Abstract

Two-dimensional field theories do not have a moduli space of vacua. Instead, it is common that their low-energy behavior is a sigma model with a target space. When this target space is compact its renormalization group flow is standard. When it is non-compact the continuous spectrum of operators can change the qualitative behavior. Here we discuss two-dimensional gauge theories with N = (2, 2) supersymmetry. We focus on two specific theories, for which we argue that they flow to free chiral multiplets at low energies: the U(1) gauge theory with one flavor (two chiral superfields with charges plus and minus one) and a non-zero Fayet-Iliopoulos term, and pure SU(N) gauge theories. We argue that the renormalization group flow of these theories has an interesting order of limits issue. Holding the position on the target space fixed, the space flattens out under the renormalization group. On the other hand, if we first go to infinity on the target space and then perform the renormalization group, we always have a non-trivial space, e.g. a cone with a deficit angle. We explain how to interpret low-energy dualities between theories with non-compact target spaces. We expect a similar qualitative behavior also for other non-compactmore »« less

Authors:

Aharony, Ofer ^[1]; Razamat, Shlomo S. ^[2]; Seiberg, Nathan ^[3]; Willett, Brian ^[4]

Weizmann Institute of Science, Rehovot (Israel)
Technion, Haifa (Israel)
Institute for Advanced Study, Princeton, NJ (United States)
Univ. of California, Santa Barbara, CA (United States)

Publication Date:: Fri Feb 10 00:00:00 EST 2017

Research Org.:: Univ. of California, San Diego, CA (United States); Weizmann Institute of Science, Rehovot (Israel)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1356084

Alternate Identifier(s):: OSTI ID: 1358379

Grant/Contract Number:: SC0009988

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: 2; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; renormalization group; supersymmetric gauge theory; supersymmetry and duality; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Aharony, Ofer, Razamat, Shlomo S., Seiberg, Nathan, and Willett, Brian. The long flow to freedom.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP02(2017)056.

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                    Aharony, Ofer, Razamat, Shlomo S., Seiberg, Nathan, & Willett, Brian. The long flow to freedom.  United States.  https://doi.org/10.1007/JHEP02(2017)056

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                    Aharony, Ofer, Razamat, Shlomo S., Seiberg, Nathan, and Willett, Brian. Fri .  
"The long flow to freedom".  United States.  https://doi.org/10.1007/JHEP02(2017)056.  https://www.osti.gov/servlets/purl/1356084.

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@article{osti_1356084,

  title        = {The long flow to freedom},

  author       = {Aharony, Ofer and Razamat, Shlomo S. and Seiberg, Nathan and Willett, Brian},

  abstractNote = {Two-dimensional field theories do not have a moduli space of vacua. Instead, it is common that their low-energy behavior is a sigma model with a target space. When this target space is compact its renormalization group flow is standard. When it is non-compact the continuous spectrum of operators can change the qualitative behavior. Here we discuss two-dimensional gauge theories with N = (2, 2) supersymmetry. We focus on two specific theories, for which we argue that they flow to free chiral multiplets at low energies: the U(1) gauge theory with one flavor (two chiral superfields with charges plus and minus one) and a non-zero Fayet-Iliopoulos term, and pure SU(N) gauge theories. We argue that the renormalization group flow of these theories has an interesting order of limits issue. Holding the position on the target space fixed, the space flattens out under the renormalization group. On the other hand, if we first go to infinity on the target space and then perform the renormalization group, we always have a non-trivial space, e.g. a cone with a deficit angle. We explain how to interpret low-energy dualities between theories with non-compact target spaces. We expect a similar qualitative behavior also for other non-compact sigma models, even when they do not flow to free theories.},

  doi          = {10.1007/JHEP02(2017)056},

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

  number       = 2,

  volume       = 2017,

  place        = {United States},

  year         = {Fri Feb 10 00:00:00 EST 2017},

  month        = {Fri Feb 10 00:00:00 EST 2017}

}

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Works referenced in this record:

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journal, August 1993

Witten, Edward
Nuclear Physics B, Vol. 403, Issue 1-2
DOI: 10.1016/0550-3213(93)90033-L

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry
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Hori, Kentaro; Kapustin, Anton
Journal of High Energy Physics, Vol. 2001, Issue 08
DOI: 10.1088/1126-6708/2001/08/045

Aspects of non-abelian gauge dynamics in two-dimensional Script N = (2,2) theories
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Hori, Kentaro; Tong, David
Journal of High Energy Physics, Vol. 2007, Issue 05
DOI: 10.1088/1126-6708/2007/05/079

Duality in two-dimensional (2,2) supersymmetric non-Abelian gauge theories
journal, October 2013

Hori, Kentaro
Journal of High Energy Physics, Vol. 2013, Issue 10
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Partition Functions of $${\mathcal{N}=(2,2)}$$ N = ( 2 , 2 ) Gauge Theories on S 2 and Vortices
journal, July 2014

Benini, Francesco; Cremonesi, Stefano
Communications in Mathematical Physics, Vol. 334, Issue 3
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Exact results in D = 2 supersymmetric gauge theories
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Doroud, Nima; Gomis, Jaume; Le Floch, Bruno
Journal of High Energy Physics, Vol. 2013, Issue 5
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Cluster Algebras from Dualities of 2d $${\mathcal{N}}$$ N = (2, 2) Quiver Gauge Theories
journal, August 2015

Benini, Francesco; Park, Daniel S.; Zhao, Peng
Communications in Mathematical Physics, Vol. 340, Issue 1
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Elliptic Genera of 2d $${\mathcal{N}}$$ N = 2 Gauge Theories
journal, November 2014

Benini, Francesco; Eager, Richard; Hori, Kentaro
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Don't panic! closed string tachyons in ALE spacetimes
journal, October 2001

Adams, Allan; Polchinski, Joseph; Silverstein, Eva
Journal of High Energy Physics, Vol. 2001, Issue 10
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Spacetime Energy Decreases under World-sheet RG Flow
journal, January 2003

Gutperle, Michael; Headrick, Matthew; Minwalla, Shiraz
Journal of High Energy Physics, Vol. 2003, Issue 01
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Mirror Symmetry and Closed String Tachyon Condensation
book, February 2005

Vafa, Cumrun
From Fields to Strings: Circumnavigating Theoretical Physics
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Renormalization group flows and continual Lie algebras
journal, August 2003

Bakas, Ioannis
Journal of High Energy Physics, Vol. 2003, Issue 08
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Irreversibility of world-sheet renormalization group flow
journal, March 2005

Oliynyk, T.; Suneeta, V.; Woolgar, E.
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Ricci flows and their integrability in two dimensions
journal, March 2005

Bakas, Ioannis
Comptes Rendus Physique, Vol. 6, Issue 2
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Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups
journal, November 2013

Benini, Francesco; Eager, Richard; Hori, Kentaro
Letters in Mathematical Physics, Vol. 104, Issue 4
DOI: 10.1007/s11005-013-0673-y

Works referencing / citing this record:

From 3d duality to 2d duality
journal, November 2017

Aharony, Ofer; Razamat, Shlomo S.; Willett, Brian
Journal of High Energy Physics, Vol. 2017, Issue 11
DOI: 10.1007/jhep11(2017)090

Seifert fibering operators in 3d N = 2 $$ \mathcal{N}=2 $$ theories
journal, November 2018

Closset, Cyril; Kim, Heeyeon; Willett, Brian
Journal of High Energy Physics, Vol. 2018, Issue 11
DOI: 10.1007/jhep11(2018)004

GLSMs, joins, and nonperturbatively-realized geometries
journal, December 2019

Knapp, Johanna; Sharpe, Eric
Journal of High Energy Physics, Vol. 2019, Issue 12
DOI: 10.1007/jhep12(2019)096

IR duality in 2D $N = (0, 2)$ gauge theory with noncompact dynamics
journal, March 2019

Dedushenko, Mykola; Gukov, Sergei
Physical Review D, Vol. 99, Issue 6
DOI: 10.1103/physrevd.99.066005

Sigma Models on Flags
text, January 2018

Ohmori, Kantaro; Seiberg, Nathan; Shao, Shu-Heng
arXiv
DOI: 10.48550/arxiv.1809.10604

GLSMs, joins, and nonperturbatively-realized geometries
text, January 2019

Knapp, Johanna; Sharpe, Eric
arXiv
DOI: 10.48550/arxiv.1907.04350

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Similar Records

Title: The long flow to freedom

Abstract

Citation Formats

Phases of N = 2 theories in two dimensions journal, August 1993

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry journal, August 2001

Aspects of non-abelian gauge dynamics in two-dimensional Script N = (2,2) theories journal, May 2007

Duality in two-dimensional (2,2) supersymmetric non-Abelian gauge theories journal, October 2013

Partition Functions of $${\mathcal{N}=(2,2)}$$ N = ( 2 , 2 ) Gauge Theories on S 2 and Vortices journal, July 2014

Exact results in D = 2 supersymmetric gauge theories journal, May 2013

Cluster Algebras from Dualities of 2d $${\mathcal{N}}$$ N = (2, 2) Quiver Gauge Theories journal, August 2015

Elliptic Genera of 2d $${\mathcal{N}}$$ N = 2 Gauge Theories journal, November 2014

Don't panic! closed string tachyons in ALE spacetimes journal, October 2001

Spacetime Energy Decreases under World-sheet RG Flow journal, January 2003

Mirror Symmetry and Closed String Tachyon Condensation book, February 2005

Renormalization group flows and continual Lie algebras journal, August 2003

Irreversibility of world-sheet renormalization group flow journal, March 2005

Ricci flows and their integrability in two dimensions journal, March 2005

Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups journal, November 2013

From 3d duality to 2d duality journal, November 2017

Seifert fibering operators in 3d N = 2 $$ \mathcal{N}=2 $$ theories journal, November 2018

GLSMs, joins, and nonperturbatively-realized geometries journal, December 2019

IR duality in 2D N = ( 0 , 2 ) gauge theory with noncompact dynamics journal, March 2019

Sigma Models on Flags text, January 2018

GLSMs, joins, and nonperturbatively-realized geometries text, January 2019

Phases of N = 2 theories in two dimensions
journal, August 1993

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry
journal, August 2001

Aspects of non-abelian gauge dynamics in two-dimensional Script N = (2,2) theories
journal, May 2007

Duality in two-dimensional (2,2) supersymmetric non-Abelian gauge theories
journal, October 2013

Partition Functions of $${\mathcal{N}=(2,2)}$$ N = ( 2 , 2 ) Gauge Theories on S 2 and Vortices
journal, July 2014

Exact results in D = 2 supersymmetric gauge theories
journal, May 2013

Cluster Algebras from Dualities of 2d $${\mathcal{N}}$$ N = (2, 2) Quiver Gauge Theories
journal, August 2015

Elliptic Genera of 2d $${\mathcal{N}}$$ N = 2 Gauge Theories
journal, November 2014

Don't panic! closed string tachyons in ALE spacetimes
journal, October 2001

Spacetime Energy Decreases under World-sheet RG Flow
journal, January 2003

Mirror Symmetry and Closed String Tachyon Condensation
book, February 2005

Renormalization group flows and continual Lie algebras
journal, August 2003

Irreversibility of world-sheet renormalization group flow
journal, March 2005

Ricci flows and their integrability in two dimensions
journal, March 2005

Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups
journal, November 2013

From 3d duality to 2d duality
journal, November 2017

Seifert fibering operators in 3d N = 2 $$ \mathcal{N}=2 $$ theories
journal, November 2018

GLSMs, joins, and nonperturbatively-realized geometries
journal, December 2019

IR duality in 2D $N = (0, 2)$ gauge theory with noncompact dynamics
journal, March 2019

Sigma Models on Flags
text, January 2018

GLSMs, joins, and nonperturbatively-realized geometries
text, January 2019