Conformal Symmetry and Effective Potential: II. Evolution

TL;DR

This paper explores how conformal symmetry can be applied to the evolution of the effective potential in $$-theory, even with mass parameters, by introducing a novel vacuum operation for calculating anomalous dimensions.

Contribution

It introduces the vacuum $V_{z,x}$-operation as a new algebraic tool to handle mass terms in conformal symmetry-based effective potential calculations.

Findings

The vacuum $V_{z,x}$-operation transforms Green functions into vacuum integrations.

Conformal symmetry remains useful for effective potential analysis with mass parameters.

The method facilitates multi-loop calculations in $$-theory.

Abstract

We present the second part of a paper series devoted to the study of the multi-loop effective potential evolution in $\varphi^4$-theory using the conformal symmetry. In this paper, we demonstrate that the conformal symmetry can still be useful for the effective potential approach even at the presence of the mass parameter. To this goal, it is necessary to introduce the special treatment of the mass terms as sorts of interaction in an asymptotical expansion of the generating functional. The introduced vacuum $V_{z,x}$-operation is the main tool to the algebraic scheme of anomalous dimension calculations. It is shown that the vacuum $V_{z,x}$-operation transforms the given Green functions to the corresponding vacuum integrations which generate the effective potential.