<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>ϕ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math> theory at seven loops

Abstract

We give a detailed account of the theory of position space renormalization using graphical functions in the case of dimensionally regularized ${\ensuremath{\phi}}^{4}$ theory in four dimensions. In this theory we calculate the beta function, the mass gamma function, and the self-energy to seven loops in the minimal subtraction scheme. The anomalous dimension $\ensuremath{\gamma}$ is calculated to loop order eight. When possible, we generalize to even dimensions $\ensuremath{\ge}4$ with particular focus on ${\ensuremath{\phi}}^{3}$ theory in six dimensions. In this theory we calculate the anomalous dimension $\ensuremath{\gamma}$ to loop order six.

Topics & Concepts