Abstract
We establish in perturbation theory the existence of fixed points along the renormalization group flow for QCD with an adjoint Weyl fermion and scalar matter reminiscent of magnetic duals of QCD [1-3]. We classify the fixed points by analyzing their basin of attraction. We discover that among these there are stable supersymmetric ones emerging from a generic nonsupersymmetric renormalization group flow once the mass operators have been properly subtracted away. We therefore conclude that four dimensional supersymmetry can emerge as a fixed point theory from a nonsupersymmetric Lagrangian. Our results suggest that supersymmetry can be viewed as an emergent phenomenon in four dimensional field theory complementing recent discoveries in lower number of dimensions [4, 5].
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References
N. Seiberg, Exact results on the space of vacua of four-dimensional SUSY gauge theories, Phys. Rev. D 49 (1994) 6857 [hep-th/9402044] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
M. Mojaza, M. Nardecchia, C. Pica and F. Sannino, Dual of QCD with One Adjoint Fermion, Phys. Rev. D 83 (2011) 065022 [arXiv:1101.1522] [INSPIRE].
S.-S. Lee, Emergence of supersymmetry at a critical point of a lattice model, Phys. Rev. B 76 (2007) 075103 [cond-mat/0611658] [INSPIRE].
S.-S. Lee, TASI Lectures on Emergence of Supersymmetry, Gauge Theory and String in Condensed Matter Systems, arXiv:1009.5127 [INSPIRE].
F. Sannino, QCD Dual, Phys. Rev. D 80 (2009) 065011 [arXiv:0907.1364] [INSPIRE].
G. ’t Hooft, Recent Developments in Gauge Theories, Plenum Press, (1980), pg. 135; reprinted in Unity of Forces in the Universe Vol. II, A. Zee ed., World Scientific, (1982), pg. 1004.
J. Terning, ’t Hooft anomaly matching for QCD, Phys. Rev. Lett. 80 (1998) 2517 [hep-th/9706074] [INSPIRE].
F. Sannino, Higher Representations Duals, Nucl. Phys. B 830 (2010) 179 [arXiv:0909.4584] [INSPIRE].
F. Sannino and K. Tuominen, Orientifold theory dynamics and symmetry breaking, Phys. Rev. D 71 (2005) 051901 [hep-ph/0405209] [INSPIRE].
D.K. Hong, S.D. Hsu and F. Sannino, Composite Higgs from higher representations, Phys. Lett. B 597 (2004) 89 [hep-ph/0406200] [INSPIRE].
H. Gies and J. Jaeckel, Chiral phase structure of QCD with many flavors, Eur. Phys. J. C 46 (2006) 433 [hep-ph/0507171] [INSPIRE].
J. Braun and H. Gies, Running coupling at finite temperature and chiral symmetry restoration in QCD, Phys. Lett. B 645 (2007) 53 [hep-ph/0512085] [INSPIRE].
J. Braun and H. Gies, Chiral phase boundary of QCD at finite temperature, JHEP 06 (2006) 024 [hep-ph/0602226] [INSPIRE].
D.D. Dietrich and F. Sannino, Conformal window of SU(N) gauge theories with fermions in higher dimensional representations, Phys. Rev. D 75 (2007) 085018 [hep-ph/0611341] [INSPIRE].
T.A. Ryttov and F. Sannino, Conformal Windows of SU(N) Gauge Theories, Higher Dimensional Representations and The Size of The Unparticle World, Phys. Rev. D 76 (2007) 105004 [arXiv:0707.3166] [INSPIRE].
T.A. Ryttov and F. Sannino, Supersymmetry inspired QCD β-function, Phys. Rev. D 78 (2008) 065001 [arXiv:0711.3745] [INSPIRE].
F. Sannino, Dynamical Stabilization of the Fermi Scale: Phase Diagram of Strongly Coupled Theories for (Minimal) Walking Technicolor and Unparticles, arXiv:0804.0182 [INSPIRE].
E. Poppitz and M. Ünsal, Conformality or confinement (II): One-flavor CFTs and mixed-representation QCD, JHEP 12 (2009) 011 [arXiv:0910.1245] [INSPIRE].
F. Sannino, Conformal Dynamics for TeV Physics and Cosmology, Acta Phys. Polon. B 40 (2009) 3533 [arXiv:0911.0931] [INSPIRE].
J. Braun and H. Gies, Scaling laws near the conformal window of many-flavor QCD, JHEP 05 (2010) 060 [arXiv:0912.4168] [INSPIRE].
O. Antipin and K. Tuominen, Resizing the Conformal Window: A β-function Ansatz, Phys. Rev. D 81 (2010) 076011 [arXiv:0909.4879] [INSPIRE].
O. Antipin and K. Tuominen, Constraints on Conformal Windows from Holographic Duals, Mod. Phys. Lett. A 26 (2011) 2227 [arXiv:0912.0674] [INSPIRE].
M. Jarvinen and F. Sannino, Holographic Conformal Window — A Bottom Up Approach, JHEP 05 (2010) 041 [arXiv:0911.2462] [INSPIRE].
M. Mojaza, C. Pica and F. Sannino, Hot Conformal Gauge Theories, Phys. Rev. D 82 (2010) 116009 [arXiv:1010.4798] [INSPIRE].
J. Alanen, K. Kajantie and K. Tuominen, Thermodynamics of quasiconformal theories from gauge/gravity duality, Phys. Rev. D 82 (2010), no. 5 055024 [arXiv:1003.5499].
H.S. Fukano and F. Sannino, Conformal window of gauge theories with four-fermion interactions and ideal walking technicolor, Phys. Rev. D 82 (2010), no. 3 035021 [arXiv:1005.3340].
C. Pica and F. Sannino, β-function and Anomalous Dimensions, Phys. Rev. D 83 (2011) 116001 [arXiv:1011.3832] [INSPIRE].
C. Pica and F. Sannino, Ultraviolet and infrared zeros of gauge theories at the four-loop order and beyond, Phys. Rev. D 83 (2011), no. 3 035013 [arXiv:1011.5917].
M.T. Frandsen, T. Pickup and M. Teper, Delineating the conformal window, Phys. Lett. B 695 (2011) 231 [arXiv:1007.1614] [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].
N. Chen, T.A. Ryttov and R. Shrock, Patterns of Dynamical Gauge Symmetry Breaking, Phys. Rev. D 82 (2010) 116006 [arXiv:1010.3736] [INSPIRE].
T.A. Ryttov and R. Shrock, Infrared Evolution and Phase Structure of a Gauge Theory Containing Different Fermion Representations, Phys. Rev. D 81 (2010) 116003 [Erratum ibid. D 82 (2010) 059903] [arXiv:1006.0421] [INSPIRE].
T.A. Ryttov and R. Shrock, Higher extended technicolor representations and fermion generations, European Physical Journal C 71 (2011) 1523 [arXiv:1005.3844].
J. Braun, C.S. Fischer and H. Gies, Beyond Miransky Scaling, Phys. Rev. D 84 (2011) 034045 [arXiv:1012.4279] [INSPIRE].
M. Jarvinen and F. Sannino, Extreme Technicolor and The Walking Critical Temperature, JHEP 02 (2011) 081 [arXiv:1009.5380] [INSPIRE].
F. Sannino, Conformal windows of Sp(2N) and SO(N ) gauge theories, Phys. Rev. D 79 (2009), no. 9 096007 [arXiv:0902.3494].
T.A. Ryttov and F. Sannino, Conformal House, Int. J. Mod. Phys. A 25 (2010) 4603 [arXiv:0906.0307] [INSPIRE].
F. Sannino, Mass deformed S parameter in conformal theories, Phys. Rev. D 82 (2010), no. 8 081701 [arXiv:1006.0207].
F. Sannino, Magnetic S Parameter, Physical Review Letters 105 (2010), no. 23 232002 [arXiv:1007.0254].
S. Di Chiara, C. Pica and F. Sannino, Flavor Dependence of the S-parameter, Phys. Lett. B 700 (2011) 229 [arXiv:1008.1267] [INSPIRE].
F. Sannino, The Standard Model is Natural as Magnetic Gauge Theory, Mod. Phys. Lett. A 26 (2011) 1763 [arXiv:1102.5100] [INSPIRE].
S.R. Coleman and E.J. Weinberg, Radiative Corrections as the Origin of Spontaneous Symmetry Breaking, Phys. Rev. D 7 (1973) 1888 [INSPIRE].
E. Gildener and S. Weinberg, Symmetry Breaking and Scalar Bosons, Phys. Rev. D 13 (1976) 3333 [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].
M.E. Machacek and M.T. Vaughn, Two Loop Renormalization Group Equations in a General Quantum Field Theory. 2. Yukawa Couplings, Nucl. Phys. B 236 (1984) 221 [INSPIRE].
M. Luo, H. Wang and Y. Xiao, Two-loop renormalization group equations in general gauge field theories, Phys. Rev. D 67 (2003), no. 6 065019 [arXiv:hep-ph/0211440].
M.J. Strassler, Nonsupersymmetric theories with light scalar fields and large hierarchies, hep-th/0309122 [INSPIRE].
H.-S. Goh, M.A. Luty and S.-P. Ng, Supersymmetry without supersymmetry, JHEP 01 (2005) 040 [hep-th/0309103] [INSPIRE].
R. Sundrum, SUSY Splits, But Then Returns, JHEP 01 (2011) 062 [arXiv:0909.5430] [INSPIRE].
S. Catterall, E. Dzienkowski, J. Giedt, A. Joseph and R. Wells, Perturbative renormalization of lattice N = 4 super Yang-Mills theory, JHEP 04 (2011) 074 [arXiv:1102.1725] [INSPIRE].
S. Catterall, Supersymmetric lattices, arXiv:1005.5346 [INSPIRE].
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Antipin, O., Mojaza, M., Pica, C. et al. Magnetic fixed points and emergent supersymmetry. J. High Energ. Phys. 2013, 37 (2013). https://doi.org/10.1007/JHEP06(2013)037
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DOI: https://doi.org/10.1007/JHEP06(2013)037