Lagrange multiplier field approach to shift-symmetric theories: the φ^4 derivative theory and the crumpled-to-flat transition of membranes at two-loop order

Preprint, 2023

Abstract:

We introduce a technique relying on the use of Lagrange multiplier field 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 φ4 derivative theory in D=4−ϵ, which is also relevant to describe the crumpled-to-flat transition of polymerized membranes. Some features of this transition are provided.

Recommended citation: "Lagrange multiplier field approach to shift-symmetric theories: the φ^4 derivative theory and the crumpled-to-flat transition of membranes at two-loop order", L. Delzescaux, C. Duclut, D. Mouhanna, M. Tissier, arXiv:2307.00600 (2023). https://arxiv.org/abs/2307.00600

arXiv version [pdf]