Abstract
We discuss non-renormalization theorems applying to galileon field theories and their generalizations. Galileon theories are similar in many respects to other derivatively coupled effective field theories, including general relativity and $P(X)$ theories. In particular, these other theories also enjoy versions of non-renormalization theorems that protect certain operators against corrections from self-loops. However, we argue that the galileons are distinguished by the fact that they are not renormalized even by loops of other heavy fields whose couplings respect the galileon symmetry.
Highlights
In this paper we focus on another property of galileons: their non-renormalization theorem
One puzzle is that the theorem is simultaneously non-trivial and trivial, in some sense. It is non-trivial in that there exists a diagrammatic proof of the theorem [30] which heavily relies on the detailed structure of the special galileon operators
These dimensional analysis arguments can be made for many other massless, derivatively-coupled theories including General Relativity (GR), P (X) theories and the conformal dilaton field
Summary
We briefly review some of the basic properties of the galileon and the nonrenormalization theorem. Many of the operators invariant under (1.1), powers of ∂2φ for example, will lead to higher order equations of motion (EOM) and will generically run afoul of Ostrogradski’s theorem [35], leading to instabilities (see [36, 37] for nice reviews) These instabilities are not problematic as long as the theory is treated as an effective field theory (EFT) [38,39,40]. Not all operators invariant under the galileon symmetry are of this type; there exist a finite number of operators which have fewer than two derivatives per field and are not constructed from the invariant building block ∂μ∂νφ They yield strictly second order equations of motion. For the remainder of the paper, we will follow common conventions and refer to the special terms in (2.1) alone as “galileons.” All other terms compatible with the galileon symmetry will be called “higher order operators.”
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