Abstract
In this paper we study multi-gravity (multi-metric and multi-vielbein) theories in the presence of cycles of interactions (cycles in the so-called `theory graph'). It has been conjectured that in multi-metric theories such cycles lead to the introduction of a ghost-like instability, which, however, is absent in the multi-vielbein version of such theories. In this paper we answer this question in the affirmative by explicitly demonstrating the presence of the ghost in such multi-metric theories in the form of dangerous higher derivative terms in the decoupling limit Lagrangian; we also explain why these terms are absent in the vielbein version of these theories. Finally we discuss the ramifications of our result on the dimensional deconstruction paradigm, which would seek an equivalence between such theories and a truncated Kaluza-Klein theory, and find that the impediment to taking the continuum limit due to a low strong-coupling scale is exacerbated by the presence of the ghost, when these theories are constructed using metrics.
Highlights
Boulware-Deser ghost [3], making the theory have an unacceptably low cutoff (generically Λ5 = (m4MPl)1/5, where m is the graviton mass), yet recently there was constructed [4,5,6,7,8,9,10,11] a theory which is ghost free, and has the higher cutoff of Λ3 = (m2MPl)1/3
We discuss the ramifications of our result on the dimensional deconstruction paradigm, which would seek an equivalence between such theories and a truncated KaluzaKlein theory, and find that the impediment to taking the continuum limit due to a low strong-coupling scale is exacerbated by the presence of the ghost, when these theories are constructed using metrics
That this difference will lead to ghosts in the metric version of the theory is demonstrated in two different ways in section 4; in section 5 we first review the vielbein version of multigravity theories, investigate the structure of interactions, and argue why the same ghost is not present there
Summary
These theories can be represented using theory graphs [14, 20, 25,26,27] in which each field corresponds to a node of the graph; a term in the action which is an interaction between two fields corresponds to an edge of the graph, and an interaction between more than two fields can be represented by using an auxiliary vertex to which all the fields concerned are connected; see figure 1 for some examples This formalism is useful as it allows one to restate certain questions about a particular theory in terms of properties of its theory graph, which is the main topic of this paper: looking at the effect of the presence of a cycle in the graph.
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