O(N) and O(N) and O(N)

Gubser, Steven S.; Jepsen, Christian; Parikh, Sarthak; Trundy, Brian

doi:10.1007/jhep11(2017)107

Title: O(N) and O(N) and O(N)

Abstract

Three related analyses of Φ⁴ theory with O(N) symmetry are presented. In the first, we review the O(N) model over the p-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking in an ultrametric context. We demonstrate the existence of a Wilson-Fisher fixed point using an ϵ expansion, and we show how to obtain leading order results for the anomalous dimensions of low dimension operators near the fixed point. Along the way, we note an important aspect of ultrametric field theories, which is a non-renormalization theorem for kinetic terms. In the second analysis, we employ large N methods to establish formulas for anomalous dimensions which are valid equally for field theories over the p-adic numbers and field theories on Rⁿ. Results for anomalous dimensions agree between the first and second analyses when they can be meaningfully compared. In the third analysis, we consider higher derivative versions of the O(N) model on Rⁿ, the simplest of which has been studied in connection with spatially modulated phases. Our general formula for anomalous dimensions can still be applied. Analogies with two-derivative theories hint at the existence of some interesting unconventional field theories in four real Euclidean dimensions.

Authors:

Gubser, Steven S. ^[1]; Jepsen, Christian ^[1]; Parikh, Sarthak ^[1]; Trundy, Brian ^[1]

Princeton Univ., Princeton, NJ (United States). Joseph Henry Lab. of Physics

Publication Date:: Fri Nov 17 00:00:00 EST 2017

Research Org.:: Princeton Univ., NJ (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1507578

Grant/Contract Number:: FG02-91ER40671

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: 11; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 1/N Expansion; Sigma Models; Renormalization Group

Citation Formats


                    Gubser, Steven S., Jepsen, Christian, Parikh, Sarthak, and Trundy, Brian. O(N) and O(N) and O(N).  United States: N. p., 2017. 
Web.  doi:10.1007/jhep11(2017)107.

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                    Gubser, Steven S., Jepsen, Christian, Parikh, Sarthak, & Trundy, Brian. O(N) and O(N) and O(N).  United States.  https://doi.org/10.1007/jhep11(2017)107

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                    Gubser, Steven S., Jepsen, Christian, Parikh, Sarthak, and Trundy, Brian. Fri .  
"O(N) and O(N) and O(N)".  United States.  https://doi.org/10.1007/jhep11(2017)107.  https://www.osti.gov/servlets/purl/1507578.

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@article{osti_1507578,

  title        = {O(N) and O(N) and O(N)},

  author       = {Gubser, Steven S. and Jepsen, Christian and Parikh, Sarthak and Trundy, Brian},

  abstractNote = {Three related analyses of Φ4 theory with O(N) symmetry are presented. In the first, we review the O(N) model over the p-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking in an ultrametric context. We demonstrate the existence of a Wilson-Fisher fixed point using an ϵ expansion, and we show how to obtain leading order results for the anomalous dimensions of low dimension operators near the fixed point. Along the way, we note an important aspect of ultrametric field theories, which is a non-renormalization theorem for kinetic terms. In the second analysis, we employ large N methods to establish formulas for anomalous dimensions which are valid equally for field theories over the p-adic numbers and field theories on Rn. Results for anomalous dimensions agree between the first and second analyses when they can be meaningfully compared. In the third analysis, we consider higher derivative versions of the O(N) model on Rn, the simplest of which has been studied in connection with spatially modulated phases. Our general formula for anomalous dimensions can still be applied. Analogies with two-derivative theories hint at the existence of some interesting unconventional field theories in four real Euclidean dimensions.},

  doi          = {10.1007/jhep11(2017)107},

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

  number       = 11,

  volume       = 2017,

  place        = {United States},

  year         = {Fri Nov 17 00:00:00 EST 2017},

  month        = {Fri Nov 17 00:00:00 EST 2017}

}

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Works referenced in this record:

Phenomenological Discussion of Magnetic Ordering in the Heavy Rare-Earth Metals
journal, October 1961

Elliott, R. J.
Physical Review, Vol. 124, Issue 2
DOI: 10.1103/PhysRev.124.346

Conformal invariance in the long-range Ising model
journal, January 2016

Paulos, Miguel F.; Rychkov, Slava; van Rees, Balt C.
Nuclear Physics B, Vol. 902
DOI: 10.1016/j.nuclphysb.2015.10.018

Investigation of the critical point in models of the type of Dyson's hierarchical models
journal, March 1973

Bleher, P. M.; Sinai, Ja. G.
Communications in Mathematical Physics, Vol. 33, Issue 1
DOI: 10.1007/BF01645604

AdS dual of the critical O(N) vector model
journal, December 2002

Klebanov, I. R.; Polyakov, A. M.
Physics Letters B, Vol. 550, Issue 3-4
DOI: 10.1016/S0370-2693(02)02980-5

Scalar models of p-adic quantum field theory and hierarchical models
journal, February 1989

Lerner, �. Yu.; Missarov, M. D.
Theoretical and Mathematical Physics, Vol. 78, Issue 2
DOI: 10.1007/BF01018683

Critical Exponents for Long-Range Interactions
journal, October 1972

Fisher, Michael E.; Ma, Shang-keng; Nickel, B. G.
Physical Review Letters, Vol. 29, Issue 14
DOI: 10.1103/PhysRevLett.29.917

Bootstrapping the O(N) archipelago
journal, November 2015

Kos, Filip; Poland, David; Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2015, Issue 11
DOI: 10.1007/JHEP11(2015)106

Existence of a phase-transition in a one-dimensional Ising ferromagnet
journal, June 1969

Dyson, Freeman J.
Communications in Mathematical Physics, Vol. 12, Issue 2
DOI: 10.1007/BF01645907

The Crossover Region Between Long-Range and Short-Range Interactions for the Critical Exponents
journal, August 2014

Brezin, E.; Parisi, G.; Ricci-Tersenghi, F.
Journal of Statistical Physics, Vol. 157, Issue 4-5
DOI: 10.1007/s10955-014-1081-0

Scaling laws for ising models near $T_{c}$
journal, June 1966

Kadanoff, Leo P.
Physics Physique Fizika, Vol. 2, Issue 6
DOI: 10.1103/PhysicsPhysiqueFizika.2.263

p-Adic AdS/CFT
journal, January 2017

Gubser, Steven S.; Knaute, Johannes; Parikh, Sarthak
Communications in Mathematical Physics, Vol. 352, Issue 3
DOI: 10.1007/s00220-016-2813-6

Recursion Relations and Fixed Points for Ferromagnets with Long-Range Interactions
journal, July 1973

Sak, J.
Physical Review B, Vol. 8, Issue 1
DOI: 10.1103/PhysRevB.8.281

p-adic numbers in physics
journal, October 1993

Brekke, L.
Physics Reports, Vol. 233, Issue 1
DOI: 10.1016/0370-1573(93)90043-D

Epsilon-expansion in the N-component ϕ 4 model
journal, March 2006

Missarov, M. D.; Stepanov, R. G.
Theoretical and Mathematical Physics, Vol. 146, Issue 3
DOI: 10.1007/s11232-006-0041-5

Critical Properties of Phi ⁴ -Theories
book, January 2001

Kleinert, Hagen; Schulte-Frohlinde, Verena
World Scientific
DOI: 10.1142/4733

Ricci curvature of graphs
journal, January 2011

Lin, Yong; Lu, Linyuan; Yau, Shing-Tung
Tohoku Mathematical Journal, Vol. 63, Issue 4
DOI: 10.2748/tmj/1325886283

Infinitely Many Commensurate Phases in a Simple Ising Model
journal, June 1980

Fisher, Michael E.; Selke, Walter
Physical Review Letters, Vol. 44, Issue 23
DOI: 10.1103/PhysRevLett.44.1502

Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior
journal, November 1971

Wilson, Kenneth G.
Physical Review B, Vol. 4, Issue 9
DOI: 10.1103/PhysRevB.4.3184

p-adic renormalization group solutions and the euclidean renormalization group conjectures
journal, February 2012

Missarov, M. D.
P-Adic Numbers, Ultrametric Analysis, and Applications, Vol. 4, Issue 2
DOI: 10.1134/S2070046612020033

Hyperscaling above the upper critical dimension
journal, December 2012

Berche, B.; Kenna, R.; Walter, J. -C.
Nuclear Physics B, Vol. 865, Issue 1
DOI: 10.1016/j.nuclphysb.2012.07.021

Critical Exponents in p-Adic ϕ4-Model
conference, January 2006

Missarov, Moukadas D.
p-ADIC MATHEMATICAL PHYSICS: 2nd International Conference, AIP Conference Proceedings
DOI: 10.1063/1.2193117

Critical Behavior at the Onset of $\vec{k}$ -Space Instability on the $λ$ Line
journal, December 1975

Hornreich, R. M.; Luban, Marshall; Shtrikman, S.
Physical Review Letters, Vol. 35, Issue 25
DOI: 10.1103/PhysRevLett.35.1678

Edge length dynamics on graphs with applications to p-adic AdS/CFT
journal, June 2017

Gubser, Steven S.; Heydeman, Matthew; Jepsen, Christian
Journal of High Energy Physics, Vol. 2017, Issue 6
DOI: 10.1007/JHEP06(2017)157

The ANNNI model — Theoretical analysis and experimental application
journal, November 1988

Selke, W.
Physics Reports, Vol. 170, Issue 4
DOI: 10.1016/0370-1573(88)90140-8

Non-archimedean string dynamics
journal, June 1988

Brekke, Lee; Freund, Peter G. O.; Olson, Mark
Nuclear Physics B, Vol. 302, Issue 3
DOI: 10.1016/0550-3213(88)90207-6

Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture
journal, November 1971

Wilson, Kenneth G.
Physical Review B, Vol. 4, Issue 9
DOI: 10.1103/PhysRevB.4.3174

Adelic string amplitudes
journal, December 1987

Freund, Peter G. O.; Witten, Edward
Physics Letters B, Vol. 199, Issue 2
DOI: 10.1016/0370-2693(87)91357-8

Higher spin gauge theory and holography: the three-point functions
journal, September 2010

Giombi, Simone; Yin, Xi
Journal of High Energy Physics, Vol. 2010, Issue 9
DOI: 10.1007/JHEP09(2010)115

The renormalization group and the ε expansion
journal, August 1974

Wilson, K.
Physics Reports, Vol. 12, Issue 2
DOI: 10.1016/0370-1573(74)90023-4

Critical Phenomena and Universal Exponents in Statistical Physics. On Dyson's Hierarchical Model
journal, April 1987

Bleher, P. M.; Major, P.
The Annals of Probability, Vol. 15, Issue 2
DOI: 10.1214/aop/1176992155

Non-archimedean strings
journal, December 1987

Freund, Peter G. O.; Olson, Mark
Physics Letters B, Vol. 199, Issue 2
DOI: 10.1016/0370-2693(87)91356-6

Infinitely Many Commensurate Phases in a Simple Ising Model.
journal, July 1980

Fisher, Michael E.; Selke, Walter
Physical Review Letters, Vol. 45, Issue 2
DOI: 10.1103/physrevlett.45.148.4

Theoretical Predictions for Critical Exponents at the λ-Point of bose Liquids
text, January 1971

D'Eramo, M.; Parisi, G.; Peliti, L.
INFN Open Access Repository
DOI: 10.15161/oar.it/1448892473.56

Hyperscaling above the upper critical dimension
text, January 2014

Berche, Bertrand; Kenna, Ralph; Walter, Jean-Charles
arXiv
DOI: 10.48550/arxiv.1402.1657

The crossover region between long-range and short-range interactions for the critical exponents
text, January 2014

Brezin, Edouard; Parisi, Giorgio; Ricci-Tersenghi, Federico
arXiv
DOI: 10.48550/arxiv.1407.3358

The Higgs Model with a Complex Ghost Pair
text, January 1993

Jansen, Karl; Kuti, Julius; Liu, Chuan
arXiv
DOI: 10.48550/arxiv.hep-lat/9305003

Computation of quark mass anomalous dimension at O(1/N_f^2) in quantum chromodynamics
text, January 1999

Ciuchini, M.; Derkachov, S. E.; Gracey, J. A.
arXiv
DOI: 10.48550/arxiv.hep-ph/9912221

Works referencing / citing this record:

p-adic Mellin amplitudes
journal, April 2019

Jepsen, Christian Baadsgaard; Parikh, Sarthak
Journal of High Energy Physics, Vol. 2019, Issue 4
DOI: 10.1007/jhep04(2019)101

Character integral representation of zeta function in AdSd+1. Part II. Application to partially-massless higher-spin gravities
journal, July 2018

Basile, Thomas; Joung, Euihun; Lal, Shailesh
Journal of High Energy Physics, Vol. 2018, Issue 7
DOI: 10.1007/jhep07(2018)132

Non-local non-linear sigma models
journal, September 2019

Gubser, Steven S.; Jepsen, Christian B.; Ji, Ziming
Journal of High Energy Physics, Vol. 2019, Issue 9
DOI: 10.1007/jhep09(2019)005

Recursion relations in p -adic Mellin Space
journal, June 2019

Jepsen, Christian Baadsgaard; Parikh, Sarthak
Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 28
DOI: 10.1088/1751-8121/ab227b

Character Integral Representation of Zeta function in AdS$_{d+1}$: II. Application to partially-massless higher-spin gravities
text, January 2018

Basile, Thomas; Joung, Euihun; Lal, Shailesh
arXiv
DOI: 10.48550/arxiv.1805.10092

Indications of isotropic Lifshitz points in four dimensions
text, January 2018

Zappala, Dario
arXiv
DOI: 10.48550/arxiv.1806.00043

Holographic dual of the five-point conformal block
text, January 2019

Parikh, Sarthak
arXiv
DOI: 10.48550/arxiv.1901.01267

Non-local non-linear sigma models
text, January 2019

Gubser, Steven S.; Jepsen, Christian B.; Ji, Ziming
arXiv
DOI: 10.48550/arxiv.1906.10281

Holography and Local Fields
journal, July 2018

Saberi, Ingmar
p-Adic Numbers, Ultrametric Analysis and Applications, Vol. 10, Issue 3
DOI: 10.1134/s2070046618030019

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Title: O(N) and O(N) and O(N)

Abstract

Citation Formats

Phenomenological Discussion of Magnetic Ordering in the Heavy Rare-Earth Metals journal, October 1961

Conformal invariance in the long-range Ising model journal, January 2016

Investigation of the critical point in models of the type of Dyson's hierarchical models journal, March 1973

AdS dual of the critical O(N) vector model journal, December 2002

Scalar models of p-adic quantum field theory and hierarchical models journal, February 1989

Critical Exponents for Long-Range Interactions journal, October 1972

Bootstrapping the O(N) archipelago journal, November 2015

Existence of a phase-transition in a one-dimensional Ising ferromagnet journal, June 1969

The Crossover Region Between Long-Range and Short-Range Interactions for the Critical Exponents journal, August 2014

Scaling laws for ising models near T c journal, June 1966

p-Adic AdS/CFT journal, January 2017

Recursion Relations and Fixed Points for Ferromagnets with Long-Range Interactions journal, July 1973

p-adic numbers in physics journal, October 1993

Epsilon-expansion in the N-component ϕ 4 model journal, March 2006

Critical Properties of Phi 4 -Theories book, January 2001

Ricci curvature of graphs journal, January 2011

Infinitely Many Commensurate Phases in a Simple Ising Model journal, June 1980

Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior journal, November 1971

p-adic renormalization group solutions and the euclidean renormalization group conjectures journal, February 2012

Hyperscaling above the upper critical dimension journal, December 2012

Critical Exponents in p-Adic ϕ4-Model conference, January 2006

Critical Behavior at the Onset of k → -Space Instability on the λ Line journal, December 1975

Edge length dynamics on graphs with applications to p-adic AdS/CFT journal, June 2017

The ANNNI model — Theoretical analysis and experimental application journal, November 1988

Non-archimedean string dynamics journal, June 1988

Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture journal, November 1971

Adelic string amplitudes journal, December 1987

Higher spin gauge theory and holography: the three-point functions journal, September 2010

The renormalization group and the ε expansion journal, August 1974

Critical Phenomena and Universal Exponents in Statistical Physics. On Dyson's Hierarchical Model journal, April 1987

Non-archimedean strings journal, December 1987

Infinitely Many Commensurate Phases in a Simple Ising Model. journal, July 1980

Theoretical Predictions for Critical Exponents at the λ-Point of bose Liquids text, January 1971

Hyperscaling above the upper critical dimension text, January 2014

The crossover region between long-range and short-range interactions for the critical exponents text, January 2014

The Higgs Model with a Complex Ghost Pair text, January 1993

Computation of quark mass anomalous dimension at O(1/N_f^2) in quantum chromodynamics text, January 1999

p-adic Mellin amplitudes journal, April 2019

Character integral representation of zeta function in AdSd+1. Part II. Application to partially-massless higher-spin gravities journal, July 2018

Non-local non-linear sigma models journal, September 2019

Recursion relations in p -adic Mellin Space journal, June 2019

Character Integral Representation of Zeta function in AdS$_{d+1}$: II. Application to partially-massless higher-spin gravities text, January 2018

Indications of isotropic Lifshitz points in four dimensions text, January 2018

Holographic dual of the five-point conformal block text, January 2019

Non-local non-linear sigma models text, January 2019

Holography and Local Fields journal, July 2018

Phenomenological Discussion of Magnetic Ordering in the Heavy Rare-Earth Metals
journal, October 1961

Conformal invariance in the long-range Ising model
journal, January 2016

Investigation of the critical point in models of the type of Dyson's hierarchical models
journal, March 1973

AdS dual of the critical O(N) vector model
journal, December 2002

Scalar models of p-adic quantum field theory and hierarchical models
journal, February 1989

Critical Exponents for Long-Range Interactions
journal, October 1972

Bootstrapping the O(N) archipelago
journal, November 2015

Existence of a phase-transition in a one-dimensional Ising ferromagnet
journal, June 1969

The Crossover Region Between Long-Range and Short-Range Interactions for the Critical Exponents
journal, August 2014

Scaling laws for ising models near $T_{c}$
journal, June 1966

p-Adic AdS/CFT
journal, January 2017

Recursion Relations and Fixed Points for Ferromagnets with Long-Range Interactions
journal, July 1973

p-adic numbers in physics
journal, October 1993

Epsilon-expansion in the N-component ϕ 4 model
journal, March 2006

Critical Properties of Phi ⁴ -Theories
book, January 2001

Ricci curvature of graphs
journal, January 2011

Infinitely Many Commensurate Phases in a Simple Ising Model
journal, June 1980

Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior
journal, November 1971

p-adic renormalization group solutions and the euclidean renormalization group conjectures
journal, February 2012

Hyperscaling above the upper critical dimension
journal, December 2012

Critical Exponents in p-Adic ϕ4-Model
conference, January 2006

Critical Behavior at the Onset of $\vec{k}$ -Space Instability on the $λ$ Line
journal, December 1975

Edge length dynamics on graphs with applications to p-adic AdS/CFT
journal, June 2017

The ANNNI model — Theoretical analysis and experimental application
journal, November 1988

Non-archimedean string dynamics
journal, June 1988

Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture
journal, November 1971

Adelic string amplitudes
journal, December 1987

Higher spin gauge theory and holography: the three-point functions
journal, September 2010

The renormalization group and the ε expansion
journal, August 1974

Critical Phenomena and Universal Exponents in Statistical Physics. On Dyson's Hierarchical Model
journal, April 1987

Non-archimedean strings
journal, December 1987

Infinitely Many Commensurate Phases in a Simple Ising Model.
journal, July 1980

Theoretical Predictions for Critical Exponents at the λ-Point of bose Liquids
text, January 1971

Hyperscaling above the upper critical dimension
text, January 2014

The crossover region between long-range and short-range interactions for the critical exponents
text, January 2014

The Higgs Model with a Complex Ghost Pair
text, January 1993

Computation of quark mass anomalous dimension at O(1/N_f^2) in quantum chromodynamics
text, January 1999

p-adic Mellin amplitudes
journal, April 2019

Character integral representation of zeta function in AdSd+1. Part II. Application to partially-massless higher-spin gravities
journal, July 2018

Non-local non-linear sigma models
journal, September 2019

Recursion relations in p -adic Mellin Space
journal, June 2019

Character Integral Representation of Zeta function in AdS$_{d+1}$: II. Application to partially-massless higher-spin gravities
text, January 2018

Indications of isotropic Lifshitz points in four dimensions
text, January 2018

Holographic dual of the five-point conformal block
text, January 2019

Non-local non-linear sigma models
text, January 2019

Holography and Local Fields
journal, July 2018