The Yang-Mills gradient flow for QCD-like theories is generalized by including a fermionic matter term in the gauge field flow equation. We combine this with two different flow equations for the fermionic degrees of freedom. The solutions for the different gradient flow setups are used in the perturbative computations of the vacuum expectation value of the Yang-Mills Lagrangian density and the field renormalization factor of the evolved fermions up to next-to-leading order in the coupling. We find a one-parameter family of flow systems for which there exists a renormalization scheme in which the evolved fermion anomalous dimension vanishes to all orders in perturbation theory. The fermion number dependence of different flows is studied and applications to lattice studies are anticipated.
M. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Phil. Trans. Roy. Soc. Lond. A 308 (1982) 523.
S.K. Donaldson, Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. Lond. Math. Soc. 50 (1985) 1.
G. Parisi and Y.-S. Wu, Perturbation theory without gauge fixing, Sci. Sin. 24 (1981) 483.
P.H. Damgaard and H. Huffel, Stochastic quantization, Phys. Rept. 152 (1987) 227 [INSPIRE].
R. Tzani, Evaluation of the chiral anomaly by the stochastic quantization method, Phys. Rev. D 33 (1986) 1146 [INSPIRE].
K. Symanzik, Schrödinger representation and Casimir effect in renormalizable quantum field theory, Nucl. Phys. B 190 (1981) 1 [INSPIRE].
W.E. Caswell, Asymptotic behavior of non-Abelian gauge theories to two loop order, Phys. Rev. Lett. 33 (1974) 244 [INSPIRE].
J.C. Collins, Renormalization: an introduction to renormalization, the renormalization group, and the operator product expansion, Cambridge University Press, Cambridge, U.K. (1986) [INSPIRE].
L.U. Ancarani and G. Gasaneo, Derivatives of any order of the Gaussian hypergeometric function 2F1 (a, b, c; a with respect to the parameters a, b and c, J. Phys. A 42 (2009) 395208 [INSPIRE].
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2011.05316
About this article
Cite this article
Boers, M. Nonminimal gradient flows in QCD-like theories. J. High Energ. Phys. 2021, 204 (2021). https://doi.org/10.1007/JHEP01(2021)204
- Lattice QCD
- Perturbative QCD
- Renormalization Group