Abstract
Higher derivative corrections are ubiquitous in effective field theories, which seemingly introduces new degrees of freedom at successive orders. This is actually an artefact of the implicit local derivative expansion defining effective field theories. We argue that higher derivative corrections that introduce additional degrees of freedom should be removed and their effects captured either by lower derivative corrections, or special combinations of higher derivative corrections not propagating extra degrees of freedom. Three methods adapted for this task are examined and field redefinitions are found to be most appropriate. First order higher derivative corrections in a scalar tensor theory are removed by field redefinition and it is found that their effects are captured by a subset of Horndeski theories. A case is made for restricting the effective field theory expansions in principle to only terms not introducing additional degrees of freedom.
Highlights
Higher derivative corrections in effective field theory (EFT) are ubiquitous, and are very hard to avoid
We argue that higher derivative corrections that introduce additional degrees of freedom should be removed and their effects captured either by lower derivative corrections, or special combinations of higher derivative corrections not propagating extra degrees of freedom
When we decide that the degrees of freedom integrated out are heavy with respect to some energy scale we are interested in, can the nonlocal terms in the action be considered small, and expanded in inverse powers of the heavy mass scale. This expansion corresponds to a local derivative expansion of the nonlocal terms, and this is how higher derivative terms appear in the low energy EFT
Summary
Higher derivative corrections in effective field theory (EFT) are ubiquitous, and are very hard to avoid. It is important to emphasize that there are theories with higher derivatives in the action that are not genuine in the sense defined above, since they contain the same number of degrees of freedom as their lower order counterparts with the same number of dynamical variables. The observation that the higher derivative terms appear perturbatively, and that their effects should be taken into account perturbatively as well, resolves the issue of extra degrees of freedom They never appear in perturbatively expandable solutions. One must discard all the solutions of the equations of motion that are not analytic in the expansion parameter as unphysical
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