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  • Letter
  • Open Access

Auxiliary fields approach to shift-symmetric theories: The φ4 derivative theory and the crumpled-to-flat transition of membranes at two-loop order

L. Delzescaux1,*, C. Duclut2,†, D. Mouhanna1,‡, and M. Tissier1,§

  • 1Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, 75005 Paris, France
  • 2Laboratoire Physico-Chimie Curie, CNRS UMR 168, Institut Curie, Université PSL, Sorbonne Université, 75005 Paris, France

  • *louise.delzescaux@sorbonne-universite.fr
  • †charlie.duclut@curie.fr
  • ‡mouhanna@lptmc.jussieu.fr
  • §tissier@lptmc.jussieu.fr
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Phys. Rev. D 108, L081702 – Published 10 October, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L081702

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 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.

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Phys. Rev. D 108, L081702– Published 10 October, 2023
  • Received 5 July 2023
  • Accepted 30 August 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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