On the field independent additive constant in Wilson actions

TL;DR

This paper examines the role of the field-independent additive constant in Wilson actions within the exact renormalization group framework, highlighting its significance for vacuum energy and providing concrete examples.

Contribution

It clarifies the importance of the additive constant in Wilson actions and its impact on the partition function and vacuum energy, with explicit examples.

Findings

The additive constant does not influence normalized correlation functions.

The constant determines the renormalized vacuum energy density.

Explicit analysis of Gaussian theory and linear sigma model in large N limit.

Abstract

We discuss the field independent additive constant in Wilson actions carefully within the exact renormalization group formalism. The additive constant does not affect the correlation functions of fields normalized by the partition function, and for that reason it is often ignored. But it is an essential part of the partition function, and in the limit where the UV cutoff goes to zero, the constant gives a renormalized vacuum energy density. We discuss two concrete examples: the Gaussian theory and the linear sigma model in the large $N$ limit.