TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysProc.7.032
TI  - A differential-geometry approach to operator mixing in massless QCD-like theories and Poincaré-Dulac theorem
PY  - 2022/06/21
UR  - https://www.scipost.org/SciPostPhysProc.7.032
JF  - SciPost Physics Proceedings
JA  - SciPost Phys. Proc.
VL  - 
IS  - 7
SP  - 032
A1  - Becchetti, Matteo
AB  - We review recent progress on operator mixing in the light of the theory of canonical forms for linear systems of differential equations and, in particular, of the Poincar\'e-Dulac theorem. We show that the matrix $A(g) = -\frac{\gamma(g)}{\beta(g)} =\frac{\gamma_0}{\beta_0}\frac{1}{g} + \cdots $ determines which different cases of operator mixing can occur, and we review their classification. We derive a sufficient condition for $A(g)$ to be set in the one-loop exact form $A(g) = \frac{\gamma_0}{\beta_0}\frac{1}{g}$. Finally, we discuss the consequences of the unitarity requirement in massless QCD-like theories, and we demonstrate that $\gamma_0$ is always diagonalizable if the theory is conformal invariant and unitary in its free limit at $g =0$.
ER  -

@Article{10.21468/SciPostPhysProc.7.032,
	title={{A differential-geometry approach to operator mixing in massless QCD-like theories and Poincaré-Dulac theorem}},
	author={Matteo Becchetti},
	journal={SciPost Phys. Proc.},
	pages={032},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhysProc.7.032},
	url={https://scipost.org/10.21468/SciPostPhysProc.7.032},
}