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

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 ${\phi }^4$ 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.

arXiv comment7 pages

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Cited by in corpus (2)

• Scale without Conformal Invariance in Dipolar Ferromagnets
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order