Composite gravitons from metric-independent quantum field theories

Abstract

We review some recent work by Carone, Erlich and Vaman on composite gravitons in metricindependent quantum field theories, with the aim of clarifying a number of basic issues. Focusing on a theory of scalar fields presented previously in the literature, we clarify the meaning of the tunings required to obtain a massless graviton. We argue that this formulation can be interpreted as the massless limit of a theory of massive composite gravitons in which the graviton mass term is not of Pauli-Fierz form. We then suggest closely related theories that can be defined without such a limiting procedure (and hence without worry about possible ghosts). Finally, we comment on the importance of finding a compelling ultraviolet completion for models of this type, and discuss some possibilities. * Invited Brief Review for Modern Physics Letters A.

Background-Independent Composite Gravity

“…Subtracting off the contribution of the clock and rod fields also served to cancel a tadpole involving derivatives of the physical fields φ a in the composite metric, in analogy with a related analysis in Ref. [13]. The cancellation of this divergent tadpole was necessary for consistency of the perturbative expansion in this approach.…”

“…(2.2), generalizing a related procedure in Ref. [13]. The clock and rod fields are nondynamical, but serve to define a coordinate basis for the vacuum spacetime.…”

“…In hindsight the reason for this is clear: a spacetime-dependent background for fields explicitly breaks diffeomorphism invariance. The clock and rod fields serve as a tool for providing a description of the vacuum about which to consider fluctuations, but ultimately they appear in the action only in terms which identically cancel one another, and do not participate in the dynamics [13].…”

Background-independent composite gravity

“…Hence, we are effectively treating g μν as an auxiliary field satisfying its classical equation of motion T μν = 0. We have introduced the clock and rod fields X M , which appear in two terms that identically cancel one another in equation (2.2), generalizing a related procedure in reference [14]. The clock and rod fields are nonphysical, but serve to define a coordinate basis for the vacuum spacetime.…”

“…In hindsight the reason for this is clear: a spacetime-dependent background for fields explicitly breaks diffeomorphism invariance. The clock and rod fields serve as a tool for providing a description of the vacuum about which to consider fluctuations, but ultimately they appear in the action only in terms which identically cancel one another, and do not participate in the dynamics [14].…”