RG flows and bifurcations
Abstract
Interpreting RG flows as dynamical systems in the space of couplings we produce a variety of constraints, global (topological) as well as local. These constraints, in turn, rule out some of the proposed RG flows and also predict new phases and fixed points, surprisingly, even in familiar theories such as model, QED3, or QCD4.
- Authors:
- Publication Date:
- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1349530
- Alternate Identifier(s):
- OSTI ID: 1426867
- Grant/Contract Number:
- SC0011632
- Resource Type:
- Published Article
- Journal Name:
- Nuclear Physics. B
- Additional Journal Information:
- Journal Name: Nuclear Physics. B Journal Volume: 919 Journal Issue: C; Journal ID: ISSN 0550-3213
- Publisher:
- Elsevier
- Country of Publication:
- Netherlands
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Gukov, Sergei. RG flows and bifurcations. Netherlands: N. p., 2017.
Web. doi:10.1016/j.nuclphysb.2017.03.025.
Gukov, Sergei. RG flows and bifurcations. Netherlands. https://doi.org/10.1016/j.nuclphysb.2017.03.025
Gukov, Sergei. Thu .
"RG flows and bifurcations". Netherlands. https://doi.org/10.1016/j.nuclphysb.2017.03.025.
@article{osti_1349530,
title = {RG flows and bifurcations},
author = {Gukov, Sergei},
abstractNote = {Interpreting RG flows as dynamical systems in the space of couplings we produce a variety of constraints, global (topological) as well as local. These constraints, in turn, rule out some of the proposed RG flows and also predict new phases and fixed points, surprisingly, even in familiar theories such as model, QED3, or QCD4.},
doi = {10.1016/j.nuclphysb.2017.03.025},
journal = {Nuclear Physics. B},
number = C,
volume = 919,
place = {Netherlands},
year = {Thu Jun 01 00:00:00 EDT 2017},
month = {Thu Jun 01 00:00:00 EDT 2017}
}
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Works referenced in this record:
The stability of the O invariant fixed point in three dimensions
journal, May 1998
- Caselle, M.; Hasenbusch, M.
- Journal of Physics A: Mathematical and General, Vol. 31, Issue 20
QCD with large number of quarks: effects of the instanton – anti-instanton pairs
journal, October 1998
- Velkovsky, M.; Shuryak, E.
- Physics Letters B, Vol. 437, Issue 3-4
Lattice study of conformal behavior in SU(3) Yang-Mills theories
journal, April 2009
- Appelquist, Thomas; Fleming, George T.; Neil, Ethan T.
- Physical Review D, Vol. 79, Issue 7
Is there a c-theorem in four dimensions?
journal, December 1988
- Cardy, John L.
- Physics Letters B, Vol. 215, Issue 4
Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II
journal, October 1961
- Nambu, Y.; Jona-Lasinio, G.
- Physical Review, Vol. 124, Issue 1
( )-Dimensional QED and a Novel Phase Transition
journal, September 1995
- Appelquist, Thomas; Terning, John; Wijewardhana, L. C. R.
- Physical Review Letters, Vol. 75, Issue 11
One, two, zero: Scales of strong interactions
journal, October 2014
- Lombardo, Maria Paola; Miura, Kohtaroh; da Silva, Tiago Nunes
- International Journal of Modern Physics A, Vol. 29, Issue 25
Conformality lost
journal, December 2009
- Kaplan, David B.; Lee, Jong-Wan; Son, Dam T.
- Physical Review D, Vol. 80, Issue 12
Influence of the full vertex and vacuum polarization on the fermion propagator in (2+1)-dimensional QED
journal, September 1996
- Maris, P.
- Physical Review D, Vol. 54, Issue 6
Chiral symmetry breaking and monopole dynamics in noncompact coupled to a four-Fermi interaction
journal, July 2010
- Armour, Wesley; Kogut, John B.; Strouthos, Costas
- Physical Review D, Vol. 82, Issue 1
Fixed point merger in the gauge beta functions
journal, December 2011
- Kusafuka, Yuki; Terao, Haruhiko
- Physical Review D, Vol. 84, Issue 12
Critical models in dimensions
journal, July 2014
- Fei, Lin; Giombi, Simone; Klebanov, Igor R.
- Physical Review D, Vol. 90, Issue 2
Phase structure of an gauge theory with flavors
journal, October 1998
- Appelquist, Thomas; Ratnaweera, Anuradha; Terning, John
- Physical Review D, Vol. 58, Issue 10
Chiral-symmetry breaking in three-dimensional electrodynamics
journal, May 1984
- Pisarski, Robert D.
- Physical Review D, Vol. 29, Issue 10
Exact five-loop renormalization group functions of θ4-theory with O(N)-symmetric and cubic interactions. Critical exponents up to ϵ5
journal, January 1995
- Kleinert, H.; Schulte-Frohlinde, V.
- Physics Letters B, Vol. 342, Issue 1-4
A new constraint on strongly coupled field theories
journal, July 1999
- Appelquist, Thomas; Cohen, Andrew G.; Schmaltz, Martin
- Physical Review D, Vol. 60, Issue 4
Witten's complex and infinite-dimensional Morse theory
journal, January 1989
- Floer, Andreas
- Journal of Differential Geometry, Vol. 30, Issue 1
Nonlinear dynamics in three-dimensional QED and nontrivial infrared structure
journal, November 1999
- Mavromatos, N. E.; Papavassiliou, J.
- Physical Review D, Vol. 60, Issue 12
Lectures on non-perturbative effects in large N gauge theories, matrix models and strings: Non-perturbative effects in large N gauge theories, matrix models and strings
journal, April 2014
- Mariño, M.
- Fortschritte der Physik, Vol. 62, Issue 5-6
Critical behavior of the mn-component field model in three dimensions II. Three-loop results
journal, December 1989
- Shpot, N. A.
- Physics Letters A, Vol. 142, Issue 8-9
Chiral phase structure of QCD with many flavors
journal, March 2006
- Gies, H.; Jaeckel, J.
- The European Physical Journal C, Vol. 46, Issue 2
Conformal or walking? Monte Carlo renormalization group studies of gauge models with fundamental fermions
journal, July 2010
- Hasenfratz, Anna
- Physical Review D, Vol. 82, Issue 1
theory of pairing pseudogap in cuprates: From -wave superconductor to antiferromagnet via an algebraic Fermi liquid
journal, August 2002
- Franz, M.; Tešanović, Z.; Vafek, O.
- Physical Review B, Vol. 66, Issue 5
Asymptotic Behavior of Non-Abelian Gauge Theories to Two-Loop Order
journal, July 1974
- Caswell, William E.
- Physical Review Letters, Vol. 33, Issue 4
The Chiral Limit of Non-compact QED3
journal, May 2003
- Hands, S. J.; Kogut, J. B.; Scorzato, L.
- Nuclear Physics B - Proceedings Supplements, Vol. 119
No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions
journal, February 2016
- Karthik, Nikhil; Narayanan, Rajamani
- Physical Review D, Vol. 93, Issue 4
Higher representations on the lattice: Numerical simulations, SU(2) with adjoint fermions
journal, May 2010
- Del Debbio, Luigi; Patella, Agostino; Pica, Claudio
- Physical Review D, Vol. 81, Issue 9
Zero Temperature Chiral Phase Transition in SU( N ) Gauge Theories
journal, August 1996
- Appelquist, Thomas; Terning, John; Wijewardhana, L. C. R.
- Physical Review Letters, Vol. 77, Issue 7
Bifurcation analysis and the Conley index in mechanics
journal, September 2012
- Bolsinov, Alexey V.; Borisov, Alexey V.; Mamaev, Ivan S.
- Regular and Chaotic Dynamics, Vol. 17, Issue 5
Critical Behavior of Anisotropic Cubic Systems
journal, November 1973
- Aharony, Amnon
- Physical Review B, Vol. 8, Issue 9
theory of underdoped high-temperature superconductors
journal, September 2002
- Herbut, Igor F.
- Physical Review B, Vol. 66, Issue 9
Conformal QED d , F -theorem and the ϵ expansion
journal, February 2016
- Giombi, Simone; Klebanov, Igor R.; Tarnopolsky, Grigory
- Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 13
Scaling and Renormalization in Statistical Physics
book, January 2015
- Cardy, John
- Cambridge University Press
Critical flavor number in the three dimensional Thirring model
journal, May 2007
- Christofi, Stavros; Hands, Simon; Strouthos, Costas
- Physical Review D, Vol. 75, Issue 10
Dirac Fermions in Solids: From High-T c Cuprates and Graphene to Topological Insulators and Weyl Semimetals
journal, March 2014
- Vafek, Oskar; Vishwanath, Ashvin
- Annual Review of Condensed Matter Physics, Vol. 5, Issue 1
Towards a renormalizable standard model without a fundamental Higgs scalar
journal, May 2004
- Gies, Holger; Jaeckel, Joerg; Wetterich, Christof
- Physical Review D, Vol. 69, Issue 10
$\mathcal{N} = 2$ quantum field theories and their BPS quivers
journal, January 2014
- Alim, Murad; Cecotti, Sergio; Córdova, Clay
- Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 1
Large N field theories, string theory and gravity
journal, January 2000
- Aharony, Ofer; Gubser, Steven S.; Maldacena, Juan
- Physics Reports, Vol. 323, Issue 3-4
Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas
journal, March 1984
- Nienhuis, Bernard
- Journal of Statistical Physics, Vol. 34, Issue 5-6
Conformal phase transition in gauge theories
journal, April 1997
- Miransky, V. A.; Yamawaki, Koichi
- Physical Review D, Vol. 55, Issue 8
Jumping out of the light-Higgs conformal window
journal, May 2013
- Antipin, Oleg; Mojaza, Matin; Sannino, Francesco
- Physical Review D, Vol. 87, Issue 9
Supersymmetry inspired QCD beta function
journal, September 2008
- Ryttov, Thomas A.; Sannino, Francesco
- Physical Review D, Vol. 78, Issue 6
Investigating the critical properties of beyond-QCD theories using Monte Carlo renormalization group matching
journal, August 2009
- Hasenfratz, Anna
- Physical Review D, Vol. 80, Issue 3
Walking beyond the rainbow
journal, February 1989
- Cohen, Andrew; Georgi, Howard
- Nuclear Physics B, Vol. 314, Issue 1
Dilaton and Chiral-Symmetry Breaking
journal, March 1986
- Bardeen, W. A.; Leung, C. N.; Love, S. T.
- Physical Review Letters, Vol. 56, Issue 12
Gauge-invariant response functions in algebraic Fermi liquids
journal, July 2003
- Franz, M.; Pereg-Barnea, T.; Sheehy, D. E.
- Physical Review B, Vol. 68, Issue 2
Effective action and conformal phase transition in three-dimensional QED
journal, September 1998
- Gusynin, V. P.; Miransky, V. A.; Shpagin, A. V.
- Physical Review D, Vol. 58, Issue 8
Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( ) Dimensions
journal, June 2016
- Mross, David F.; Alicea, Jason; Motrunich, Olexei I.
- Physical Review Letters, Vol. 117, Issue 1
Gradient formula for the beta function of 2D quantum field theory
journal, May 2010
- Friedan, Daniel; Konechny, Anatoly
- Journal of Physics A: Mathematical and Theoretical, Vol. 43, Issue 21
Morse Theory, the Conley Index and Floer Homology
journal, March 1990
- Salamon, Dietmar
- Bulletin of the London Mathematical Society, Vol. 22, Issue 2
Twelve massless flavors and three colors below the conformal window
journal, September 2011
- Fodor, Zoltán; Holland, Kieran; Kuti, Julius
- Physics Letters B, Vol. 703, Issue 3
Chiral symmetry breaking in three-dimensional quantum electrodynamics in the presence of irrelevant interactions: A renormalization group study
journal, May 2005
- Kaveh, Kamran; Herbut, Igor F.
- Physical Review B, Vol. 71, Issue 18
The connection matrix theory for Morse decompositions
journal, February 1989
- Franzosa, Robert D.
- Transactions of the American Mathematical Society, Vol. 311, Issue 2
Parity violation and gauge noninvariance of the effective gauge field action in three dimensions
journal, May 1984
- Redlich, A. N.
- Physical Review D, Vol. 29, Issue 10
Infrared fixed point in SU(2) gauge theory with adjoint fermions
journal, April 2011
- DeGrand, Thomas; Shamir, Yigal; Svetitsky, Benjamin
- Physical Review D, Vol. 83, Issue 7
Postmodern Technicolor
journal, October 1997
- Appelquist, Thomas; Terning, John; Wijewardhana, L. C. R.
- Physical Review Letters, Vol. 79, Issue 15
Critical Behavior in (2+1)-Dimensional QED
journal, June 1988
- Appelquist, Thomas; Nash, Daniel; Wijewardhana, L. C. R.
- Physical Review Letters, Vol. 60, Issue 25
Quantum Electrodynamics in from the Expansion
journal, April 2016
- Di Pietro, Lorenzo; Komargodski, Zohar; Shamir, Itamar
- Physical Review Letters, Vol. 116, Issue 13
Spontaneous breaking of Lorentz symmetry in ( )-dimensional QED
journal, November 2016
- Janssen, Lukas
- Physical Review D, Vol. 94, Issue 9
Unconventional Integer Quantum Hall Effect in Graphene
journal, September 2005
- Gusynin, V. P.; Sharapov, S. G.
- Physical Review Letters, Vol. 95, Issue 14
Running coupling and mass anomalous dimension of SU(3) gauge theory with two flavors of symmetric-representation fermions
journal, September 2010
- DeGrand, Thomas; Shamir, Yigal; Svetitsky, Benjamin
- Physical Review D, Vol. 82, Issue 5
The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999
- Maldacena, Juan
- International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133
Dynamical symmetry breaking and particle mass generation in gauge field theories
journal, May 1983
- Fomin, P. I.; Gusynin, V. P.; Miransky, V. A.
- La Rivista Del Nuovo Cimento Series 3, Vol. 6, Issue 5
Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators
journal, June 2016
- Metlitski, Max A.; Vishwanath, Ashvin
- Physical Review B, Vol. 93, Issue 24
Critical phenomena and renormalization-group theory
journal, October 2002
- Pelissetto, Andrea; Vicari, Ettore
- Physics Reports, Vol. 368, Issue 6
Critical number of fermions in three-dimensional QED
journal, December 2016
- Gusynin, V. P.; Pyatkovskiy, P. K.
- Physical Review D, Vol. 94, Issue 12
Stability of a three-dimensional cubic fixed point in the two-coupling-constant theory
journal, December 1997
- Kleinert, H.; Thoms, S.; Schulte-Frohlinde, V.
- Physical Review B, Vol. 56, Issue 22
Dynamical chiral symmetry breaking in unquenched
journal, October 2004
- Fischer, C. S.; Alkofer, R.; Dahm, T.
- Physical Review D, Vol. 70, Issue 7
Beyond Miransky scaling
journal, August 2011
- Braun, Jens; Fischer, Christian S.; Gies, Holger
- Physical Review D, Vol. 84, Issue 3
Remarks on the chiral phase transition in chromodynamics
journal, January 1984
- Pisarski, Robert D.; Wilczek, Frank
- Physical Review D, Vol. 29, Issue 2
Scaling theory of the Potts-model multicritical point
journal, September 1980
- Cardy, John L.; Nauenberg, M.; Scalapino, D. J.
- Physical Review B, Vol. 22, Issue 5
On the phase structure of vector-like gauge theories with massless fermions
journal, March 1982
- Banks, T.; Zaks, A.
- Nuclear Physics B, Vol. 196, Issue 2
Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I
journal, April 1961
- Nambu, Y.; Jona-Lasinio, G.
- Physical Review, Vol. 122, Issue 1
Phase diagram of compact QED coupled to a four-Fermi interaction
journal, February 2003
- Kogut, John B.; Strouthos, Costas G.
- Physical Review D, Vol. 67, Issue 3
Phase structure of many-flavor
journal, August 2014
- Braun, Jens; Gies, Holger; Janssen, Lukas
- Physical Review D, Vol. 90, Issue 3
Running coupling at finite temperature and chiral symmetry restoration in QCD
journal, February 2007
- Braun, Jens; Gies, Holger
- Physics Letters B, Vol. 645, Issue 1
Lattice Study of the Conformal Window in QCD-like Theories
journal, April 2008
- Appelquist, Thomas; Fleming, George T.; Neil, Ethan T.
- Physical Review Letters, Vol. 100, Issue 17
Lyapunov maps, simplicial complexes and the Stone functor
journal, March 1992
- Robbin, Joel W.; Salamon, Dietmar A.
- Ergodic Theory and Dynamical Systems, Vol. 12, Issue 1
Stokes’ phenomenon; smoothing a victorian discontinuity
journal, January 1988
- Berry, M. V.
- Publications mathématiques de l'IHÉS, Vol. 68, Issue 1
Critical behavior of the ( )-dimensional Thirring model
journal, November 2012
- Janssen, Lukas; Gies, Holger
- Physical Review D, Vol. 86, Issue 10
Quark confinement and number of flavors in strong coupling lattice QCD
journal, July 1992
- Iwasaki, Y.; Kanaya, K.; Sakai, S.
- Physical Review Letters, Vol. 69, Issue 1
Connected simple systems and the Conley index of isolated invariant sets
journal, January 1985
- Salamon, Dietmar
- Transactions of the American Mathematical Society, Vol. 291, Issue 1
Inverse Landau-Khalatnikov transformation and infrared critical exponents of (2+1)-dimensional quantum electrodynamics
journal, June 1997
- Aitchison, I. J. R.; Mavromatos, N. E.; Mc Neill, D.
- Physics Letters B, Vol. 402, Issue 1-2
Non-compact QED3 with Nf⩾2
journal, November 2002
- Hands, S. J.; Kogut, J. B.; Strouthos, C. G.
- Nuclear Physics B, Vol. 645, Issue 1-2
Three loop analysis of the critical models in dimensions
journal, February 2015
- Fei, Lin; Giombi, Simone; Klebanov, Igor R.
- Physical Review D, Vol. 91, Issue 4
The non-abelian Coulomb phase of the gauged vector model at large N
journal, January 1999
- Rhedin, Henric; Schnitzer, Howard J.
- Nuclear Physics B, Vol. 537, Issue 1-3