Abstract
We consider the most general perturbatively renormalizable theory of vector fields in four dimensions with a global SU(N) symmetry and massless couplings. The Lagrangian contains 1 quadratic, 2 cubic and 4 quartic couplings. The RG flow among this set of 7 couplings is computed to 1-loop and a rich phase diagram is mapped out; in particular it is shown that a finite number of asymptotically free RG-flows exist corresponding to non-trivial fixed points for the ratios of the couplings. None of these are gauge theories, i.e. possess only global SU(N) invariance but not a local one. We also include the most general ghost couplings, still with global SU(N) invariance, and compute the RG flow to 1-loop for all 9 resulting couplings. Again asymptotically free RG flows exist with non-trivial fixed points for the ratios of couplings. It is shown that Yang-Mills theory emerges at a particular fixed point. The theories at the other fixed points are marginally relevant gauge symmetry violating perturbations of Yang-Mills theory. The large-N limit is also investigated in detail.
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J. Iliopoulos, D. V. Nanopoulos and T. N. Tomaras, Infrared stability or anti grand unification, Phys. Lett. B 94 (1980) 141 [INSPIRE].
D. Förster, H. B. Nielsen and M. Ninomiya, Dynamical Stability of Local Gauge Symmetry: Creation of Light from Chaos, Phys. Lett. B 94 (1980) 135 [INSPIRE].
S. Catterall, D. Ferrante and A. Nicholson, de Sitter gravity from lattice gauge theory, Eur. Phys. J. Plus 127 (2012) 101 [arXiv:0912.5525] [INSPIRE].
R. Jackiw and S. Y. Pi, Tutorial on Scale and Conformal Symmetries in Diverse Dimensions, J. Phys. A 44 (2011) 223001 [arXiv:1101.4886] [INSPIRE].
S. El-Showk, Y. Nakayama and S. Rychkov, What Maxwell Theory in D ≠ 4 teaches us about scale and conformal invariance, Nucl. Phys. B 848 (2011) 578 [arXiv:1101.5385] [INSPIRE].
Y. Nakayama, Scale invariance vs conformal invariance, Phys. Rept. 569 (2015) 1 [arXiv:1302.0884] [INSPIRE].
L. Fei, S. Giombi and I. R. Klebanov, Critical O(N) models in 6 − ϵ dimensions, Phys. Rev. D 90 (2014) 025018 [arXiv:1404.1094] [INSPIRE].
J. A. M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
J. Kuipers, T. Ueda, J. A. M. Vermaseren and J. Vollinga, FORM version 4.0, Comput. Phys. Commun. 184 (2013) 1453 [arXiv:1203.6543] [INSPIRE].
B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE].
G. ’t Hooft and M. J. G. Veltman, Regularization and Renormalization of Gauge Fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
G. ’t Hooft, Dimensional regularization and the renormalization group, Nucl. Phys. B 61 (1973) 455 [INSPIRE].
W. A. Bardeen, A. J. Buras, D. W. Duke and T. Muta, Deep Inelastic Scattering Beyond the Leading Order in Asymptotically Free Gauge Theories, Phys. Rev. D 18 (1978) 3998 [INSPIRE].
D. J. Gross and F. Wilczek, Asymptotically Free Gauge Theories — I, Phys. Rev. D 8 (1973) 3633 [INSPIRE].
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Nogradi, D. Vector fields, RG flows and emergent gauge symmetry. J. High Energ. Phys. 2021, 44 (2021). https://doi.org/10.1007/JHEP05(2021)044
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DOI: https://doi.org/10.1007/JHEP05(2021)044