RG flows and bifurcations

Gukov, Sergei

doi:10.1016/j.nuclphysb.2017.03.025

Title: RG flows and bifurcations

Journal Article · Thu Jun 01 00:00:00 EDT 2017 · Nuclear Physics. B

DOI:https://doi.org/10.1016/j.nuclphysb.2017.03.025· OSTI ID:1349530

Gukov, Sergei

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.

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

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

Grant/Contract Number:: SC0011632

OSTI ID:: 1349530

Alternate ID(s):: OSTI ID: 1426867

Journal Information:: Nuclear Physics. B, Journal Name: Nuclear Physics. B Vol. 919 Journal Issue: C; ISSN 0550-3213

Publisher:: ElsevierCopyright Statement

Country of Publication:: Netherlands

Language:: English

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Cited by: 56 works

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References (87)

The stability of the O invariant fixed point in three dimensions Caselle, M.; Hasenbusch, M. Journal of Physics A: Mathematical and General, Vol. 31, Issue 20 https://doi.org/10.1088/0305-4470/31/20/004	journal	May 1998
QCD with large number of quarks: effects of the instanton – anti-instanton pairs Velkovsky, M.; Shuryak, E. Physics Letters B, Vol. 437, Issue 3-4 https://doi.org/10.1016/S0370-2693(98)00930-7	journal	October 1998
Lattice study of conformal behavior in SU(3) Yang-Mills theories Appelquist, Thomas; Fleming, George T.; Neil, Ethan T. Physical Review D, Vol. 79, Issue 7 https://doi.org/10.1103/PhysRevD.79.076010	journal	April 2009
Is there a c-theorem in four dimensions? Cardy, John L. Physics Letters B, Vol. 215, Issue 4 https://doi.org/10.1016/0370-2693(88)90054-8	journal	December 1988
Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II Nambu, Y.; Jona-Lasinio, G. Physical Review, Vol. 124, Issue 1 https://doi.org/10.1103/PhysRev.124.246	journal	October 1961
( $2 + 1$ )-Dimensional QED and a Novel Phase Transition Appelquist, Thomas; Terning, John; Wijewardhana, L. C. R. Physical Review Letters, Vol. 75, Issue 11 https://doi.org/10.1103/PhysRevLett.75.2081	journal	September 1995
One, two, zero: Scales of strong interactions Lombardo, Maria Paola; Miura, Kohtaroh; da Silva, Tiago Nunes International Journal of Modern Physics A, Vol. 29, Issue 25 https://doi.org/10.1142/S0217751X14450079	journal	October 2014
Conformality lost Kaplan, David B.; Lee, Jong-Wan; Son, Dam T. Physical Review D, Vol. 80, Issue 12 https://doi.org/10.1103/PhysRevD.80.125005	journal	December 2009
Influence of the full vertex and vacuum polarization on the fermion propagator in (2+1)-dimensional QED Maris, P. Physical Review D, Vol. 54, Issue 6 https://doi.org/10.1103/PhysRevD.54.4049	journal	September 1996
Chiral symmetry breaking and monopole dynamics in noncompact ${QED}_{3}$ coupled to a four-Fermi interaction Armour, Wesley; Kogut, John B.; Strouthos, Costas Physical Review D, Vol. 82, Issue 1 https://doi.org/10.1103/PhysRevD.82.014503	journal	July 2010
Fixed point merger in the $S U (N)$ gauge beta functions Kusafuka, Yuki; Terao, Haruhiko Physical Review D, Vol. 84, Issue 12 https://doi.org/10.1103/PhysRevD.84.125006	journal	December 2011
Critical $O (N)$ models in $6 - ε$ dimensions Fei, Lin; Giombi, Simone; Klebanov, Igor R. Physical Review D, Vol. 90, Issue 2 https://doi.org/10.1103/PhysRevD.90.025018	journal	July 2014
Phase structure of an $SU (N)$ gauge theory with $N_{f}$ flavors Appelquist, Thomas; Ratnaweera, Anuradha; Terning, John Physical Review D, Vol. 58, Issue 10 https://doi.org/10.1103/PhysRevD.58.105017	journal	October 1998
Chiral-symmetry breaking in three-dimensional electrodynamics Pisarski, Robert D. Physical Review D, Vol. 29, Issue 10 https://doi.org/10.1103/PhysRevD.29.2423	journal	May 1984
Exact five-loop renormalization group functions of θ4-theory with O(N)-symmetric and cubic interactions. Critical exponents up to ϵ5 Kleinert, H.; Schulte-Frohlinde, V. Physics Letters B, Vol. 342, Issue 1-4 https://doi.org/10.1016/0370-2693(94)01377-O	journal	January 1995
A new constraint on strongly coupled field theories Appelquist, Thomas; Cohen, Andrew G.; Schmaltz, Martin Physical Review D, Vol. 60, Issue 4 https://doi.org/10.1103/PhysRevD.60.045003	journal	July 1999
Witten's complex and infinite-dimensional Morse theory Floer, Andreas Journal of Differential Geometry, Vol. 30, Issue 1 https://doi.org/10.4310/jdg/1214443291	journal	January 1989
Nonlinear dynamics in three-dimensional QED and nontrivial infrared structure Mavromatos, N. E.; Papavassiliou, J. Physical Review D, Vol. 60, Issue 12 https://doi.org/10.1103/PhysRevD.60.125008	journal	November 1999
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 Mariño, M. Fortschritte der Physik, Vol. 62, Issue 5-6 https://doi.org/10.1002/prop.201400005	journal	April 2014
Critical behavior of the mn-component field model in three dimensions II. Three-loop results Shpot, N. A. Physics Letters A, Vol. 142, Issue 8-9 https://doi.org/10.1016/0375-9601(89)90517-3	journal	December 1989
Chiral phase structure of QCD with many flavors Gies, H.; Jaeckel, J. The European Physical Journal C, Vol. 46, Issue 2 https://doi.org/10.1140/epjc/s2006-02475-0	journal	March 2006
Conformal or walking? Monte Carlo renormalization group studies of $S U (3)$ gauge models with fundamental fermions Hasenfratz, Anna Physical Review D, Vol. 82, Issue 1 https://doi.org/10.1103/PhysRevD.82.014506	journal	July 2010
${QED}_{3}$ theory of pairing pseudogap in cuprates: From $d$ -wave superconductor to antiferromagnet via an algebraic Fermi liquid Franz, M.; Tešanović, Z.; Vafek, O. Physical Review B, Vol. 66, Issue 5 https://doi.org/10.1103/PhysRevB.66.054535	journal	August 2002
Asymptotic Behavior of Non-Abelian Gauge Theories to Two-Loop Order Caswell, William E. Physical Review Letters, Vol. 33, Issue 4 https://doi.org/10.1103/PhysRevLett.33.244	journal	July 1974
The Chiral Limit of Non-compact QED3 Hands, S. J.; Kogut, J. B.; Scorzato, L. Nuclear Physics B - Proceedings Supplements, Vol. 119 https://doi.org/10.1016/S0920-5632(03)01735-3	journal	May 2003
No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions Karthik, Nikhil; Narayanan, Rajamani Physical Review D, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevD.93.045020	journal	February 2016
Higher representations on the lattice: Numerical simulations, SU(2) with adjoint fermions Del Debbio, Luigi; Patella, Agostino; Pica, Claudio Physical Review D, Vol. 81, Issue 9 https://doi.org/10.1103/PhysRevD.81.094503	journal	May 2010
Zero Temperature Chiral Phase Transition in SU( N ) Gauge Theories Appelquist, Thomas; Terning, John; Wijewardhana, L. C. R. Physical Review Letters, Vol. 77, Issue 7 https://doi.org/10.1103/PhysRevLett.77.1214	journal	August 1996
Bifurcation analysis and the Conley index in mechanics Bolsinov, Alexey V.; Borisov, Alexey V.; Mamaev, Ivan S. Regular and Chaotic Dynamics, Vol. 17, Issue 5 https://doi.org/10.1134/S1560354712050073	journal	September 2012
Critical Behavior of Anisotropic Cubic Systems Aharony, Amnon Physical Review B, Vol. 8, Issue 9 https://doi.org/10.1103/PhysRevB.8.4270	journal	November 1973
${QED}_{3}$ theory of underdoped high-temperature superconductors Herbut, Igor F. Physical Review B, Vol. 66, Issue 9 https://doi.org/10.1103/PhysRevB.66.094504	journal	September 2002
Conformal QED _d , F -theorem and the ϵ expansion Giombi, Simone; Klebanov, Igor R.; Tarnopolsky, Grigory Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 13 https://doi.org/10.1088/1751-8113/49/13/135403	journal	February 2016
Scaling and Renormalization in Statistical Physics Cardy, John Cambridge University Press https://doi.org/10.1017/CBO9781316036440	book	January 2015
Critical flavor number in the three dimensional Thirring model Christofi, Stavros; Hands, Simon; Strouthos, Costas Physical Review D, Vol. 75, Issue 10 https://doi.org/10.1103/PhysRevD.75.101701	journal	May 2007
Dirac Fermions in Solids: From High-T _c Cuprates and Graphene to Topological Insulators and Weyl Semimetals Vafek, Oskar; Vishwanath, Ashvin Annual Review of Condensed Matter Physics, Vol. 5, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031113-133841	journal	March 2014
Towards a renormalizable standard model without a fundamental Higgs scalar Gies, Holger; Jaeckel, Joerg; Wetterich, Christof Physical Review D, Vol. 69, Issue 10 https://doi.org/10.1103/PhysRevD.69.105008	journal	May 2004
$\mathcal{N} = 2$ quantum field theories and their BPS quivers Alim, Murad; Cecotti, Sergio; Córdova, Clay Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 1 https://doi.org/10.4310/ATMP.2014.v18.n1.a2	journal	January 2014
Large N field theories, string theory and gravity Aharony, Ofer; Gubser, Steven S.; Maldacena, Juan Physics Reports, Vol. 323, Issue 3-4 https://doi.org/10.1016/S0370-1573(99)00083-6	journal	January 2000
Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas Nienhuis, Bernard Journal of Statistical Physics, Vol. 34, Issue 5-6 https://doi.org/10.1007/BF01009437	journal	March 1984
Conformal phase transition in gauge theories Miransky, V. A.; Yamawaki, Koichi Physical Review D, Vol. 55, Issue 8 https://doi.org/10.1103/PhysRevD.55.5051	journal	April 1997
Jumping out of the light-Higgs conformal window Antipin, Oleg; Mojaza, Matin; Sannino, Francesco Physical Review D, Vol. 87, Issue 9 https://doi.org/10.1103/PhysRevD.87.096005	journal	May 2013
Supersymmetry inspired QCD beta function Ryttov, Thomas A.; Sannino, Francesco Physical Review D, Vol. 78, Issue 6 https://doi.org/10.1103/PhysRevD.78.065001	journal	September 2008
Investigating the critical properties of beyond-QCD theories using Monte Carlo renormalization group matching Hasenfratz, Anna Physical Review D, Vol. 80, Issue 3 https://doi.org/10.1103/PhysRevD.80.034505	journal	August 2009
Walking beyond the rainbow Cohen, Andrew; Georgi, Howard Nuclear Physics B, Vol. 314, Issue 1 https://doi.org/10.1016/0550-3213(89)90109-0	journal	February 1989
Dilaton and Chiral-Symmetry Breaking Bardeen, W. A.; Leung, C. N.; Love, S. T. Physical Review Letters, Vol. 56, Issue 12 https://doi.org/10.1103/PhysRevLett.56.1230	journal	March 1986
Gauge-invariant response functions in algebraic Fermi liquids Franz, M.; Pereg-Barnea, T.; Sheehy, D. E. Physical Review B, Vol. 68, Issue 2 https://doi.org/10.1103/PhysRevB.68.024508	journal	July 2003
Effective action and conformal phase transition in three-dimensional QED Gusynin, V. P.; Miransky, V. A.; Shpagin, A. V. Physical Review D, Vol. 58, Issue 8 https://doi.org/10.1103/PhysRevD.58.085023	journal	September 1998
Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( $2 + 1$ ) Dimensions Mross, David F.; Alicea, Jason; Motrunich, Olexei I. Physical Review Letters, Vol. 117, Issue 1 https://doi.org/10.1103/PhysRevLett.117.016802	journal	June 2016
Gradient formula for the beta function of 2D quantum field theory Friedan, Daniel; Konechny, Anatoly Journal of Physics A: Mathematical and Theoretical, Vol. 43, Issue 21 https://doi.org/10.1088/1751-8113/43/21/215401	journal	May 2010
Morse Theory, the Conley Index and Floer Homology Salamon, Dietmar Bulletin of the London Mathematical Society, Vol. 22, Issue 2 https://doi.org/10.1112/blms/22.2.113	journal	March 1990
Twelve massless flavors and three colors below the conformal window Fodor, Zoltán; Holland, Kieran; Kuti, Julius Physics Letters B, Vol. 703, Issue 3 https://doi.org/10.1016/j.physletb.2011.07.037	journal	September 2011
Chiral symmetry breaking in three-dimensional quantum electrodynamics in the presence of irrelevant interactions: A renormalization group study Kaveh, Kamran; Herbut, Igor F. Physical Review B, Vol. 71, Issue 18 https://doi.org/10.1103/PhysRevB.71.184519	journal	May 2005
The connection matrix theory for Morse decompositions Franzosa, Robert D. Transactions of the American Mathematical Society, Vol. 311, Issue 2 https://doi.org/10.1090/S0002-9947-1989-0978368-7	journal	February 1989
Parity violation and gauge noninvariance of the effective gauge field action in three dimensions Redlich, A. N. Physical Review D, Vol. 29, Issue 10 https://doi.org/10.1103/PhysRevD.29.2366	journal	May 1984
Infrared fixed point in SU(2) gauge theory with adjoint fermions DeGrand, Thomas; Shamir, Yigal; Svetitsky, Benjamin Physical Review D, Vol. 83, Issue 7 https://doi.org/10.1103/PhysRevD.83.074507	journal	April 2011
Postmodern Technicolor Appelquist, Thomas; Terning, John; Wijewardhana, L. C. R. Physical Review Letters, Vol. 79, Issue 15 https://doi.org/10.1103/PhysRevLett.79.2767	journal	October 1997
Critical Behavior in (2+1)-Dimensional QED Appelquist, Thomas; Nash, Daniel; Wijewardhana, L. C. R. Physical Review Letters, Vol. 60, Issue 25 https://doi.org/10.1103/PhysRevLett.60.2575	journal	June 1988
Quantum Electrodynamics in $d = 3$ from the $ε$ Expansion Di Pietro, Lorenzo; Komargodski, Zohar; Shamir, Itamar Physical Review Letters, Vol. 116, Issue 13 https://doi.org/10.1103/PhysRevLett.116.131601	journal	April 2016
Spontaneous breaking of Lorentz symmetry in ( $2 + ε$ )-dimensional QED Janssen, Lukas Physical Review D, Vol. 94, Issue 9 https://doi.org/10.1103/PhysRevD.94.094013	journal	November 2016
Unconventional Integer Quantum Hall Effect in Graphene Gusynin, V. P.; Sharapov, S. G. Physical Review Letters, Vol. 95, Issue 14 https://doi.org/10.1103/PhysRevLett.95.146801	journal	September 2005
Running coupling and mass anomalous dimension of SU(3) gauge theory with two flavors of symmetric-representation fermions DeGrand, Thomas; Shamir, Yigal; Svetitsky, Benjamin Physical Review D, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRevD.82.054503	journal	September 2010
The Large-N Limit of Superconformal Field Theories and Supergravity Maldacena, Juan International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133 https://doi.org/10.1023/A:1026654312961	journal	January 1999
Dynamical symmetry breaking and particle mass generation in gauge field theories Fomin, P. I.; Gusynin, V. P.; Miransky, V. A. La Rivista Del Nuovo Cimento Series 3, Vol. 6, Issue 5 https://doi.org/10.1007/BF02740014	journal	May 1983
Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators Metlitski, Max A.; Vishwanath, Ashvin Physical Review B, Vol. 93, Issue 24 https://doi.org/10.1103/PhysRevB.93.245151	journal	June 2016
Critical phenomena and renormalization-group theory Pelissetto, Andrea; Vicari, Ettore Physics Reports, Vol. 368, Issue 6 https://doi.org/10.1016/S0370-1573(02)00219-3	journal	October 2002
Critical number of fermions in three-dimensional QED Gusynin, V. P.; Pyatkovskiy, P. K. Physical Review D, Vol. 94, Issue 12 https://doi.org/10.1103/PhysRevD.94.125009	journal	December 2016
Stability of a three-dimensional cubic fixed point in the two-coupling-constant $φ^{4}$ theory Kleinert, H.; Thoms, S.; Schulte-Frohlinde, V. Physical Review B, Vol. 56, Issue 22 https://doi.org/10.1103/PhysRevB.56.14428	journal	December 1997
Dynamical chiral symmetry breaking in unquenched ${Q E D}_{3}$ Fischer, C. S.; Alkofer, R.; Dahm, T. Physical Review D, Vol. 70, Issue 7 https://doi.org/10.1103/PhysRevD.70.073007	journal	October 2004
Beyond Miransky scaling Braun, Jens; Fischer, Christian S.; Gies, Holger Physical Review D, Vol. 84, Issue 3 https://doi.org/10.1103/PhysRevD.84.034045	journal	August 2011
Remarks on the chiral phase transition in chromodynamics Pisarski, Robert D.; Wilczek, Frank Physical Review D, Vol. 29, Issue 2 https://doi.org/10.1103/PhysRevD.29.338	journal	January 1984
Scaling theory of the Potts-model multicritical point Cardy, John L.; Nauenberg, M.; Scalapino, D. J. Physical Review B, Vol. 22, Issue 5 https://doi.org/10.1103/PhysRevB.22.2560	journal	September 1980
On the phase structure of vector-like gauge theories with massless fermions Banks, T.; Zaks, A. Nuclear Physics B, Vol. 196, Issue 2 https://doi.org/10.1016/0550-3213(82)90035-9	journal	March 1982
Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I Nambu, Y.; Jona-Lasinio, G. Physical Review, Vol. 122, Issue 1 https://doi.org/10.1103/PhysRev.122.345	journal	April 1961
Phase diagram of compact QED coupled to a four-Fermi interaction Kogut, John B.; Strouthos, Costas G. Physical Review D, Vol. 67, Issue 3 https://doi.org/10.1103/PhysRevD.67.034504	journal	February 2003
Phase structure of many-flavor ${QED}_{3}$ Braun, Jens; Gies, Holger; Janssen, Lukas Physical Review D, Vol. 90, Issue 3 https://doi.org/10.1103/PhysRevD.90.036002	journal	August 2014
Running coupling at finite temperature and chiral symmetry restoration in QCD Braun, Jens; Gies, Holger Physics Letters B, Vol. 645, Issue 1 https://doi.org/10.1016/j.physletb.2006.11.059	journal	February 2007
Lattice Study of the Conformal Window in QCD-like Theories Appelquist, Thomas; Fleming, George T.; Neil, Ethan T. Physical Review Letters, Vol. 100, Issue 17 https://doi.org/10.1103/PhysRevLett.100.171607	journal	April 2008
Lyapunov maps, simplicial complexes and the Stone functor Robbin, Joel W.; Salamon, Dietmar A. Ergodic Theory and Dynamical Systems, Vol. 12, Issue 1 https://doi.org/10.1017/S0143385700006647	journal	March 1992
Stokes’ phenomenon; smoothing a victorian discontinuity Berry, M. V. Publications mathématiques de l'IHÉS, Vol. 68, Issue 1 https://doi.org/10.1007/BF02698550	journal	January 1988
Critical behavior of the ( $2 + 1$ )-dimensional Thirring model Janssen, Lukas; Gies, Holger Physical Review D, Vol. 86, Issue 10 https://doi.org/10.1103/PhysRevD.86.105007	journal	November 2012
Quark confinement and number of flavors in strong coupling lattice QCD Iwasaki, Y.; Kanaya, K.; Sakai, S. Physical Review Letters, Vol. 69, Issue 1 https://doi.org/10.1103/PhysRevLett.69.21	journal	July 1992
Connected simple systems and the Conley index of isolated invariant sets Salamon, Dietmar Transactions of the American Mathematical Society, Vol. 291, Issue 1 https://doi.org/10.1090/S0002-9947-1985-0797044-3	journal	January 1985
Inverse Landau-Khalatnikov transformation and infrared critical exponents of (2+1)-dimensional quantum electrodynamics Aitchison, I. J. R.; Mavromatos, N. E.; Mc Neill, D. Physics Letters B, Vol. 402, Issue 1-2 https://doi.org/10.1016/S0370-2693(97)00447-4	journal	June 1997
Non-compact QED3 with Nf⩾2 Hands, S. J.; Kogut, J. B.; Strouthos, C. G. Nuclear Physics B, Vol. 645, Issue 1-2 https://doi.org/10.1016/S0550-3213(02)00869-6	journal	November 2002
Prospects of Inflation Linde, Andrei Physica Scripta https://doi.org/10.1238/Physica.Topical.117a00040	journal	January 2005
Three loop analysis of the critical $O (N)$ models in $6 - ε$ dimensions Fei, Lin; Giombi, Simone; Klebanov, Igor R. Physical Review D, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevD.91.045011	journal	February 2015
The non-abelian Coulomb phase of the gauged vector model at large N Rhedin, Henric; Schnitzer, Howard J. Nuclear Physics B, Vol. 537, Issue 1-3 https://doi.org/10.1016/S0550-3213(98)00610-5	journal	January 1999

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