Auxiliary fields approach to shift-symmetric theories: the $\varphi^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order

TL;DR

This paper introduces an auxiliary field technique to simplify high-order renormalization group calculations in shift-symmetric derivative theories, demonstrated through two-loop RG equations and membrane transition analysis.

Contribution

The paper presents a novel auxiliary field method that streamlines the computation of fluctuations in shift-symmetric derivative theories, including applications to membrane transitions.

Findings

Derived two-loop RG equations for the $\

Analyzed the crumpled-to-flat transition of membranes at two-loop order.

Provided insights into features of the membrane transition.

Abstract

We introduce a technique relying on the use of auxiliary fields in order to eliminate explicit field-derivatives that plague the high orders renormalization group treatment of shift-symmetric, derivative, theories. This technique simplifies drastically the computation of fluctuations in such theories. This is illustrated by deriving the two-loop renormalization group equations and the three-loop anomalous dimension of the $\varphi^4$ derivative theory in $D=4-\epsilon$, which is also relevant to describe the crumpled-to-flat transition of polymerized membranes. Some features of this transition are provided.