Abstract
The ultraviolet completion of gauge theories by higher derivative terms can dramatically change their behavior at high energies. The requirement of asymptotic freedom imposes very stringent constraints that are only satisfied by a small family of higher derivative theories. If the number of derivatives is large enough (n > 4) the theory is strongly interacting both at extreme infrared and ultraviolet regimes whereas it remains asymptotically free for a low number of extra derivatives (n ⩽ 4). In all cases the theory improves its ultraviolet behavior leading in some cases to ultraviolet finite theories with vanishing β-function. The usual consistency problems associated to the presence of extra ghosts in higher derivative theories may not harm asymptotically free theories because in that case the effective masses of such ghosts are running to infinity in the ultraviolet limit.
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References
A. A. Slavnov, Invariant regularization of nonlinear chiral theories, Nucl. Phys. B 31 (1971) 301 [INSPIRE].
A. A. Slavnov, Invariant regularization of gauge theories, Theor. Math. Phys. 13 (1972) 1064 [Teor. Mat. Fiz. 13 (1972) 174] [INSPIRE].
B. W. Lee and J. Zinn-Justin, Spontaneously broken gauge symmetries. Part 1: preliminaries, Phys. Rev. D 5 (1972) 3121 [INSPIRE].
K. S. Stelle, Classical gravity with higher derivatives, Gen. Rel. Grav. 9 (1978) 353 [INSPIRE].
K. S. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
A. A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. B 91 (1980) 99 [Adv. Ser. Astrophys. Cosmol. 3 (1987) 130] [INSPIRE].
E. S. Fradkin and A. A. Tseytlin, Renormalizable asymptotically free quantum theory of gravity, Nucl. Phys. B 201 (1982) 469 [INSPIRE].
M. Asorey, J. L. Lopez and I. L. Shapiro, Some remarks on high derivative quantum gravity, Int. J. Mod. Phys. A 12 (1997) 5711 [hep-th/9610006] [INSPIRE].
M. Asorey, L. Rachwal and I. L. Shapiro, Unitary issues in some higher derivative field theories, Galaxies 6 (2018) 23 [arXiv:1802.01036] [INSPIRE].
T. Lee and G. Wick, Negative metric and the unitarity of the S-matrix, Nucl. Phys. B 9 (1969) 209.
T. D. Lee and G. C. Wick, Finite theory of quantum electrodynamics, Phys. Rev. D 2 (1970) 1033 [INSPIRE].
D. Anselmi and M. Piva, Perturbative unitarity of Lee-Wick quantum field theory, Phys. Rev. D 96 (2017) 045009 [arXiv:1703.05563] [INSPIRE].
D. Anselmi and M. Piva, A new formulation of Lee-Wick quantum field theory, JHEP 06 (2017) 066 [arXiv:1703.04584] [INSPIRE].
T. Biswas, E. Gerwick, T. Koivisto and A. Mazumdar, Towards singularity and ghost free theories of gravity, Phys. Rev. Lett. 108 (2012) 031101 [arXiv:1110.5249] [INSPIRE].
T. Biswas, A. Conroy, A. S. Koshelev and A. Mazumdar, Generalized ghost-free quadratic curvature gravity, Class. Quant. Grav. 31 (2014) 015022 [Erratum ibid. 31 (2014) 159501] [arXiv:1308.2319] [INSPIRE].
M. Asorey and F. Falceto, Geometric regularization of gauge theories, Nucl. Phys. B 327 (1989) 427 [INSPIRE].
M. Asorey and F. Falceto, On the consistency of the regularization of gauge theories by high covariant derivatives, Phys. Rev. D 54 (1996) 5290 [hep-th/9502025] [INSPIRE].
O. Babelon and M. A. Namazie, Comment on the ghost problem in a higher derivative Yang-Mills theory, J. Phys. A 13 (1980) L27 [INSPIRE].
L. Modesto and L. Rachwal, Super-renormalizable and finite gravitational theories, Nucl. Phys. B 889 (2014) 228 [arXiv:1407.8036] [INSPIRE].
L. Modesto and L. Rachwał, Universally finite gravitational and gauge theories, Nucl. Phys. B 900 (2015) 147 [arXiv:1503.00261] [INSPIRE].
L. Modesto, M. Piva and L. Rachwal, Finite quantum gauge theories, Phys. Rev. D 94 (2016) 025021 [arXiv:1506.06227] [INSPIRE].
Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
P. I. Pronin and K. V. Stepanyants, One-loop divergences in theories with an arbitrary nonminimal operator in curved space, Theor. Math. Phys. 110 (1997) 277 [Teor. Mat. Fiz. 110 (1997) 351] [INSPIRE].
D. M. Ghilencea, Higher dimensional operators and their effects in (non) supersymmetric models, Mod. Phys. Lett. A 23 (2008) 711 [arXiv:0708.2501] [INSPIRE].
M. Asorey, L. Rachwal and I. Shapiro, a-theorem in higher derivative gauge theories, in preparation.
A. O. Barvinsky and G. A. Vilkovisky, The generalized Schwinger-Dewitt technique in gauge theories and quantum gravity, Phys. Rept. 119 (1985) 1 [INSPIRE].
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Asorey, M., Falceto, F. & Rachwał, L. Asymptotic freedom and higher derivative gauge theories. J. High Energ. Phys. 2021, 75 (2021). https://doi.org/10.1007/JHEP05(2021)075
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DOI: https://doi.org/10.1007/JHEP05(2021)075