Counting RG flows

Gukov, Sergei

doi:10.1007/JHEP01(2016)020

Title: Counting RG flows

Abstract

Here, interpreting renormalization group flows as solitons interpolating between different fixed points, we ask various questions that are normally asked in soliton physics but not in renormalization theory. Can one count RG flows? Are there different "topological sectors" for RG flows? What is the moduli space of an RG flow, and how does it compare to familiar moduli spaces of (supersymmetric) dowain walls? Analyzing these questions in a wide variety of contexts -- from counting RG walls to AdS/CFT correspondence -- will not only provide favorable answers, but will also lead us to a unified general framework that is powerful enough to account for peculiar RG flows and predict new physical phenomena. Namely, using Bott's version of Morse theory we relate the topology of conformal manifolds to certain properties of RG flows that can be used as precise diagnostics and "topological obstructions" for the strong form of the C-theorem in any dimension. Moreover, this framework suggests a precise mechanism for how the violation of the strong C-theorem happens and predicts "phase transitions" along the RG flow when the topological obstruction is non-trivial. Along the way, we also find new conformal manifolds in well-known 4d CFT's and point out connections withmore »« less

Authors:

Gukov, Sergei ^[1]

California Inst. of Technology (CalTech), Pasadena, CA (United States); Max-Planck-Institut fur Mathematik, Bonn (Germany)

Publication Date:: Tue Jan 05 00:00:00 EST 2016

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

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

OSTI Identifier:: 1327329

Grant/Contract Number:: SC0011632

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: 2016; Journal Issue: 1; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; supersymmetric gauge theory; renormalization group

Citation Formats


                    Gukov, Sergei. Counting RG flows.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP01(2016)020.

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                    Gukov, Sergei. Counting RG flows.  United States.  https://doi.org/10.1007/JHEP01(2016)020

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                    Gukov, Sergei. Tue .  
"Counting RG flows".  United States.  https://doi.org/10.1007/JHEP01(2016)020.  https://www.osti.gov/servlets/purl/1327329.

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@article{osti_1327329,

  title        = {Counting RG flows},

  author       = {Gukov, Sergei},

  abstractNote = {Here, interpreting renormalization group flows as solitons interpolating between different fixed points, we ask various questions that are normally asked in soliton physics but not in renormalization theory. Can one count RG flows? Are there different "topological sectors" for RG flows? What is the moduli space of an RG flow, and how does it compare to familiar moduli spaces of (supersymmetric) dowain walls? Analyzing these questions in a wide variety of contexts -- from counting RG walls to AdS/CFT correspondence -- will not only provide favorable answers, but will also lead us to a unified general framework that is powerful enough to account for peculiar RG flows and predict new physical phenomena. Namely, using Bott's version of Morse theory we relate the topology of conformal manifolds to certain properties of RG flows that can be used as precise diagnostics and "topological obstructions" for the strong form of the C-theorem in any dimension. Moreover, this framework suggests a precise mechanism for how the violation of the strong C-theorem happens and predicts "phase transitions" along the RG flow when the topological obstruction is non-trivial. Along the way, we also find new conformal manifolds in well-known 4d CFT's and point out connections with the superconformal index and classifying spaces of global symmetry groups.},

  doi          = {10.1007/JHEP01(2016)020},

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

  number       = 1,

  volume       = 2016,

  place        = {United States},

  year         = {Tue Jan 05 00:00:00 EST 2016},

  month        = {Tue Jan 05 00:00:00 EST 2016}

}

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Title: Counting RG flows

Abstract

Citation Formats

The renormalization group and the ε expansion journal, August 1974

Gradient properties of the renormalisation group equations in multicomponent systems journal, July 1975

Is there a c-theorem in four dimensions? journal, December 1988

Evidence for the strongest version of the 4d a-theorem via a-maximization along RG flows journal, December 2004

On renormalization group flows in four dimensions journal, December 2011

Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions journal, October 2007

Exactly marginal deformations and global symmetries journal, June 2010

A note on the holographic beta and C functions journal, May 2000

Nondegenerate Critical Manifolds journal, September 1954

Naturalness versus supersymmetric non-renormalization theorems journal, December 1993

Supersymmetry and Morse theory journal, January 1982

The Yang-Mills Equations over Riemann Surfaces journal, March 1983

Stochastic Differential Equations on Two-Dimensional Theory Space and Morse Theory journal, April 1989

c-Theorem and the topology of 2D QFTs journal, September 1988

Domain walls, black holes, and supersymmetric quantum mechanics journal, May 2001

On Conformal Deformations journal, September 2002

On dangerous irrelevant operators journal, May 1982

On duality in supersymmetric Yang-Mills theory journal, July 1995

New RG fixed points and duality in supersymmetric SP(Nc) and SO(Nc) gauge theories journal, August 1995

Chiral rings, singularity theory and electric-magnetic duality journal, January 1996

Accidental symmetries and N = 1 duality in supersymmetric gauge theory journal, July 1997

Δa curiosities in some 4d susy RG flows journal, November 2012

Defects and bulk perturbations of boundary Landau-Ginzburg orbifolds journal, April 2008

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

RG flow in N = 1 discrete series journal, April 1989

Algebraic geometry and effective lagrangians journal, February 1989

Catastrophes and the classification of conformal theories journal, February 1989

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory journal, September 1994

Electric-magnetic duality in supersymmetric non-Abelian gauge theories journal, February 1995

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

Renormalization group flows from holography: Supersymmetry and a $c$-theorem journal, January 1999

Domain Walls and Flow Equations in Supergravity journal, May 2001

B-type defects in Landau-Ginzburg models journal, August 2007

A new supersymmetric index journal, November 1992

Scattering and thermodynamics of fractionally-charged supersymmetric solitons journal, March 1992

Walls, lines, and spectral dualities in 3d gauge theories journal, May 2014

Matter coupled AdS3 supergravities and their black strings journal, May 2000

Chern–Simons supergravity plus matter near the boundary of AdS3 journal, June 2001

Gauged locally supersymmetric D=3 nonlinear sigma models journal, November 2003

Renormalization Group Flows from D = 3, N = 2 Matter Coupled Gauged Supergravities journal, November 2002

Gauge theory correlators from non-critical string theory journal, May 1998

Anti de Sitter space and holography journal, January 1998

Towards a derivation of holographic entanglement entropy journal, May 2011

Aspects of N = 2 supersymmetric gauge theories in three dimensions journal, August 1997

On mirror symmetry in three dimensional Abelian gauge theories journal, April 1999

Indices for superconformal field theories in 3, 5 and 6 dimensions journal, February 2008

Exactly marginal operators and duality in four dimensional N = 1 supersymmetric gauge theory journal, July 1995

Central charges and U(1) R symmetries in Script N = 1 super Yang-Mills journal, November 2003

RG fixed points and flows in SQCD with adjoints journal, January 2004

The $ \mathcal{N} $ = 1 superconformal index for class $ \mathcal{S} $ fixed points journal, April 2014

New phenomena in SU(3) supersymmetric gauge theory journal, August 1995

Central charges and RG flow of strongly-coupled $ \mathcal{N}=2 $ theory journal, March 2013

Towards a derivation of holographic entanglement entropy text, January 2011

Superconformal indices of three-dimensional theories related by mirror symmetry text, January 2011

On Renormalization Group Flows in Four Dimensions text, January 2011

A Note on the Holographic Beta and C Functions text, January 2000

On Conformal Deformations text, January 2002

Gauged locally supersymmetric D=3 nonlinear sigma models text, January 2003

RG Fixed Points and Flows in SQCD with Adjoints text, January 2003

A New Supersymmetric Index text, January 1992

Phases of $N=2$ Theories In Two Dimensions text, January 1993

Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories text, January 1994

A Comment on Duality in N=1 Supersymmetric Non -- Abelian Gauge Theories text, January 1995

New RG Fixed Points and Duality in Supersymmetric SP(N_c) and SO(N_c) Gauge Theories text, January 1995

Accidental Symmetries and N=1 Duality in Supersymmetric Gauge Theory text, January 1996

Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions text, January 1997

Gauge Theory Correlators from Non-Critical String Theory text, January 1998

Anti De Sitter Space And Holography text, January 1998

Renormalization Group Flows from Holography--Supersymmetry and a c-Theorem text, January 1999

Properties of the new N$$ \mathcal{N} $$ = 1 AdS4 vacuum of maximal supergravity journal, January 2020

Holographic RG flows for four-dimensional N = 2 $$ \mathcal{N}=2 $$ SCFTs journal, June 2018

Anyonic Chains, Topological Defects, and Conformal Field Theory journal, October 2017

SQED 3 and SQCD 3 : Phase transitions and integrability journal, September 2019

Landscape of Simple Superconformal Field Theories in 4d text, January 2018

The renormalization group and the ε expansion
journal, August 1974

Gradient properties of the renormalisation group equations in multicomponent systems
journal, July 1975

Is there a c-theorem in four dimensions?
journal, December 1988

Evidence for the strongest version of the 4d a-theorem via a-maximization along RG flows
journal, December 2004

On renormalization group flows in four dimensions
journal, December 2011

Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions
journal, October 2007

Exactly marginal deformations and global symmetries
journal, June 2010

A note on the holographic beta and C functions
journal, May 2000

Nondegenerate Critical Manifolds
journal, September 1954

Naturalness versus supersymmetric non-renormalization theorems
journal, December 1993

Supersymmetry and Morse theory
journal, January 1982

The Yang-Mills Equations over Riemann Surfaces
journal, March 1983

Stochastic Differential Equations on Two-Dimensional Theory Space and Morse Theory
journal, April 1989

c-Theorem and the topology of 2D QFTs
journal, September 1988

Domain walls, black holes, and supersymmetric quantum mechanics
journal, May 2001

On Conformal Deformations
journal, September 2002

On dangerous irrelevant operators
journal, May 1982

On duality in supersymmetric Yang-Mills theory
journal, July 1995

New RG fixed points and duality in supersymmetric SP(Nc) and SO(Nc) gauge theories
journal, August 1995

Chiral rings, singularity theory and electric-magnetic duality
journal, January 1996

Accidental symmetries and N = 1 duality in supersymmetric gauge theory
journal, July 1997

Δa curiosities in some 4d susy RG flows
journal, November 2012

Defects and bulk perturbations of boundary Landau-Ginzburg orbifolds
journal, April 2008

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

RG flow in N = 1 discrete series
journal, April 1989

Algebraic geometry and effective lagrangians
journal, February 1989

Catastrophes and the classification of conformal theories
journal, February 1989

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
journal, September 1994

Electric-magnetic duality in supersymmetric non-Abelian gauge theories
journal, February 1995

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Renormalization group flows from holography: Supersymmetry and a $c$-theorem
journal, January 1999

Domain Walls and Flow Equations in Supergravity
journal, May 2001

B-type defects in Landau-Ginzburg models
journal, August 2007

A new supersymmetric index
journal, November 1992

Scattering and thermodynamics of fractionally-charged supersymmetric solitons
journal, March 1992

Walls, lines, and spectral dualities in 3d gauge theories
journal, May 2014

Matter coupled AdS3 supergravities and their black strings
journal, May 2000

Chern–Simons supergravity plus matter near the boundary of AdS3
journal, June 2001

Gauged locally supersymmetric D=3 nonlinear sigma models
journal, November 2003

Renormalization Group Flows from D = 3, N = 2 Matter Coupled Gauged Supergravities
journal, November 2002

Gauge theory correlators from non-critical string theory
journal, May 1998

Anti de Sitter space and holography
journal, January 1998

Towards a derivation of holographic entanglement entropy
journal, May 2011

Aspects of N = 2 supersymmetric gauge theories in three dimensions
journal, August 1997

On mirror symmetry in three dimensional Abelian gauge theories
journal, April 1999

Indices for superconformal field theories in 3, 5 and 6 dimensions
journal, February 2008

Exactly marginal operators and duality in four dimensional N = 1 supersymmetric gauge theory
journal, July 1995

Central charges and U(1) _R symmetries in Script N = 1 super Yang-Mills
journal, November 2003

RG fixed points and flows in SQCD with adjoints
journal, January 2004

The $ \mathcal{N} $ = 1 superconformal index for class $ \mathcal{S} $ fixed points
journal, April 2014

New phenomena in SU(3) supersymmetric gauge theory
journal, August 1995

Central charges and RG flow of strongly-coupled $ \mathcal{N}=2 $ theory
journal, March 2013

Towards a derivation of holographic entanglement entropy
text, January 2011

Superconformal indices of three-dimensional theories related by mirror symmetry
text, January 2011

On Renormalization Group Flows in Four Dimensions
text, January 2011

A Note on the Holographic Beta and C Functions
text, January 2000

On Conformal Deformations
text, January 2002

Gauged locally supersymmetric D=3 nonlinear sigma models
text, January 2003

RG Fixed Points and Flows in SQCD with Adjoints
text, January 2003

A New Supersymmetric Index
text, January 1992

Phases of $N=2$ Theories In Two Dimensions
text, January 1993

Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
text, January 1994

A Comment on Duality in N=1 Supersymmetric Non -- Abelian Gauge Theories
text, January 1995

New RG Fixed Points and Duality in Supersymmetric SP(N_c) and SO(N_c) Gauge Theories
text, January 1995

Accidental Symmetries and N=1 Duality in Supersymmetric Gauge Theory
text, January 1996

Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
text, January 1997

Gauge Theory Correlators from Non-Critical String Theory
text, January 1998

Anti De Sitter Space And Holography
text, January 1998

Renormalization Group Flows from Holography--Supersymmetry and a c-Theorem
text, January 1999

Properties of the new N$$ \mathcal{N} $$ = 1 AdS4 vacuum of maximal supergravity
journal, January 2020

Holographic RG flows for four-dimensional N = 2 $$ \mathcal{N}=2 $$ SCFTs
journal, June 2018

Anyonic Chains, Topological Defects, and Conformal Field Theory
journal, October 2017

${SQED}_{3}$ and ${SQCD}_{3}$ : Phase transitions and integrability
journal, September 2019

Landscape of Simple Superconformal Field Theories in 4d
text, January 2018