Abstract
We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in d = 4 + ϵ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD d and then we add Yukawa interactions and scalars which we study at next-to- and next-to-next-to-leading order. Interacting infrared fixed points naturally emerge in dimensions lower than four while ultraviolet ones appear above four. We also analyse the stability of the scalar potential for the discovered fixed points. We argue for a very rich phase diagram in three dimensions while in dimensions higher than four certain Gauge-Yukawa theories are ultraviolet complete because of the emergence of an asymptotically safe fixed point.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Giombi, I.R. Klebanov and G. Tarnopolsky, Conformal QED d , F -Theorem and the ϵ Expansion, J. Phys. A 49 (2016) 135403 [arXiv:1508.06354] [INSPIRE].
V.A. Miransky and I.A. Shovkovy, Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals, Phys. Rept. 576 (2015) 1 [arXiv:1503.00732] [INSPIRE].
L. Di Pietro, Z. Komargodski, I. Shamir and E. Stamou, Quantum Electrodynamics in d = 3 from the ε Expansion, Phys. Rev. Lett. 116 (2016) 131601 [arXiv:1508.06278] [INSPIRE].
F. Sannino, Polyakov loops versus hadronic states, Phys. Rev. D 66 (2002) 034013 [hep-ph/0204174] [INSPIRE].
A. Mócsy , F. Sannino and K. Tuominen, Confinement versus chiral symmetry, Phys. Rev. Lett. 92 (2004) 182302 [hep-ph/0308135] [INSPIRE].
F. Sannino and K. Tuominen, Tetracritical behavior in strongly interacting theories, Phys. Rev. D 70 (2004) 034019 [hep-ph/0403175] [INSPIRE].
A. Eichhorn, D. Mesterházy and M.M. Scherer, Multicritical behavior in models with two competing order parameters, Phys. Rev. E 88 (2013) 042141 [arXiv:1306.2952] [INSPIRE].
A. Eichhorn, D. Mesterházy and M.M. Scherer, Stability of fixed points and generalized critical behavior in multifield models, Phys. Rev. E 90 (2014) 052129 [arXiv:1407.7442] [INSPIRE].
A. Eichhorn, T. Helfer, D. Mesterházy and M.M. Scherer, Discovering and quantifying nontrivial fixed points in multi-field models, Eur. Phys. J. C 76 (2016) 88 [arXiv:1510.04807] [INSPIRE].
M.E. Peskin, Critical Point Behavior Of The Wilson Loop, Phys. Lett. B 94 (1980) 161 [INSPIRE].
T. Appelquist, H.-C. Cheng and B.A. Dobrescu, Bounds on universal extra dimensions, Phys. Rev. D 64 (2001) 035002 [hep-ph/0012100] [INSPIRE].
H. Gies, Renormalizability of gauge theories in extra dimensions, Phys. Rev. D 68 (2003) 085015 [hep-th/0305208] [INSPIRE].
T.R. Morris, Renormalizable extra-dimensional models, JHEP 01 (2005) 002 [hep-ph/0410142] [INSPIRE].
D.I. Kazakov and G.S. Vartanov, Renormalizable 1/N (f ) Expansion for Field Theories in Extra Dimensions, JHEP 06 (2007) 081 [arXiv:0707.2564] [INSPIRE].
A. Codello and R. Percacci, Fixed Points of Nonlinear σ-models in d > 2, Phys. Lett. B 672 (2009) 280 [arXiv:0810.0715] [INSPIRE].
F. Freire and D.F. Litim, Charge crossover at the U(1) Higgs phase transition, Phys. Rev. D 64 (2001) 045014 [hep-ph/0002153] [INSPIRE].
D.F. Litim, Fixed points of quantum gravity, Phys. Rev. Lett. 92 (2004) 201301 [hep-th/0312114] [INSPIRE].
P. Fischer and D.F. Litim, Fixed points of quantum gravity in extra dimensions, Phys. Lett. B 638 (2006) 497 [hep-th/0602203] [INSPIRE].
K. Falls, Renormalization of Newton’s constant, Phys. Rev. D 92 (2015) 124057 [arXiv:1501.05331] [INSPIRE].
D.F. Litim and F. Sannino, Asymptotic safety guaranteed, JHEP 12 (2014) 178 [arXiv:1406.2337] [INSPIRE].
D.F. Litim, M. Mojaza and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, JHEP 01 (2016) 081 [arXiv:1501.03061] [INSPIRE].
D.H. Rischke and F. Sannino, Thermodynamics of asymptotically safe theories, Phys. Rev. D 92 (2015) 065014 [arXiv:1505.07828] [INSPIRE].
K. Intriligator and F. Sannino, Supersymmetric asymptotic safety is not guaranteed, JHEP 11 (2015) 023 [arXiv:1508.07411] [INSPIRE].
S.P. Martin and J.D. Wells, Constraints on ultraviolet stable fixed points in supersymmetric gauge theories, Phys. Rev. D 64 (2001) 036010 [hep-ph/0011382] [INSPIRE].
F. Sannino, α s at LHC: Challenging asymptotic freedom, arXiv:1511.09022 [INSPIRE].
O. Svendsen, H. Bazrafshan Moghaddam and R. Brandenberger, Preheating in an Asymptotically Safe Quantum Field Theory, arXiv:1603.02628 [INSPIRE].
N.G. Nielsen, F. Sannino and O. Svendsen, Inflation from Asymptotically Safe Theories, Phys. Rev. D 91 (2015) 103521 [arXiv:1503.00702] [INSPIRE].
O. Antipin, M. Gillioz, E. Mølgaard and F. Sannino, The a theorem for gauge-Yukawa theories beyond Banks-Zaks fixed point, Phys. Rev. D 87 (2013) 125017 [arXiv:1303.1525] [INSPIRE].
I. Jack and H. Osborn, Analogs for the c Theorem for Four-dimensional Renormalizable Field Theories, Nucl. Phys. B 343 (1990) 647 [INSPIRE].
H. Osborn, Derivation of a Four-dimensional c Theorem, Phys. Lett. B 222 (1989) 97 [INSPIRE].
T. Banks and A. Zaks, On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions, Nucl. Phys. B 196 (1982) 189 [INSPIRE].
F. Sannino, Conformal Dynamics for TeV Physics and Cosmology, Acta Phys. Polon. B 40 (2009) 3533 [arXiv:0911.0931] [INSPIRE].
T.A. Ryttov and R. Shrock, Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions, Phys. Rev. D 83 (2011) 056011 [arXiv:1011.4542] [INSPIRE].
C. Pica and F. Sannino, UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond, Phys. Rev. D 83 (2011) 035013 [arXiv:1011.5917] [INSPIRE].
J.A. Gracey, The QCD β-function at O(1/N (f )), Phys. Lett. B 373 (1996) 178 [hep-ph/9602214] [INSPIRE].
M.E. Machacek and M.T. Vaughn, Two Loop Renormalization Group Equations in a General Quantum Field Theory. 1. Wave Function Renormalization, Nucl. Phys. B 222 (1983) 83 [INSPIRE].
J.K. Esbensen, T.A. Ryttov and F. Sannino, Quantum critical behavior of semisimple gauge theories, Phys. Rev. D 93 (2016) 045009 [arXiv:1512.04402] [INSPIRE].
O. Antipin, E. Mølgaard and F. Sannino, Higgs Critical Exponents and Conformal Bootstrap in Four Dimensions, JHEP 06 (2015) 030 [arXiv:1406.6166] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1603.03462
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Codello, A., Langæble, K., Litim, D.F. et al. Conformal gauge-Yukawa theories away from four dimensions. J. High Energ. Phys. 2016, 118 (2016). https://doi.org/10.1007/JHEP07(2016)118
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2016)118