Abstract

Many strongly coupled field theories admit a spectrum of gauge-invariant bound states that includes scalar particles with the same quantum numbers as the vacuum. The challenge naturally arises of how to characterise them. In particular, how can a dilaton — the pseudo-Nambu-Goldstone boson associated with approximate scale invariance — be distinguished from other generic light scalars with the same quantum numbers? We address this problem within the context of gauge-gravity dualities, by analysing the fluctuations of the higher-dimensional gravitational theory. The diagnostic test that we propose consists of comparing the results of the complete calculation, performed by using gauge-invariant fluctuations in the bulk, with the results obtained in the probe approximation. While the former captures the mixing between scalar and metric degrees of freedom, the latter removes by hand the fluctuations that source the dilatation operator of the boundary field- theory. Hence, the probe approximation cannot capture a possible light dilaton, while it should fare well for other scalar particles. We test this idea on a number of holographic models, among which are some of the best known, complete gravity backgrounds constructed within the top-down approach to gauge-gravity dualities. We compute the spectra of scalar and tensor fluctuations, that are interpreted as bound states (glueballs) of the dual field theory, and we highlight those cases in which the probe approximation yields results close to the correct physical ones, as well as those cases where significant discrepancies emerge. We interpret the latter occurrence as an indication that identifying one of the lightest scalar states with the dilaton is legitimate, at least as a leading-order approximation.

Highlights

  • We test this idea on a number of holographic models, among which are some of the best known, complete gravity backgrounds constructed within the top-down approach to gauge-gravity dualities

  • How can a dilaton — the pseudo-Nambu-Goldstone boson associated with approximate scale invariance — be distinguished from other generic light scalars with the same quantum numbers? We address this problem within the context of gauge-gravity dualities, by analysing the fluctuations of the higher-dimensional gravitational theory

  • What type of fundamental fourdimensional theories yield a dilaton in the spectrum? What are the phenomenologically measurable and distinctive properties of such a particle? Could it be that the Higgs particle is at the fundamental level a composite dilaton emerging from a strongly coupled field theory? And above all stands the question we address in this paper: how can one distinguish between adilaton and other generic light scalar particles, that have the same quantum numbers? We will address this question in the restricted context of models that can be studied with the tools provided by gauge-gravity dualities

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Summary

Five-dimensional holographic formalism

We consider five-dimensional sigma-models of n scalars coupled to gravity. We adopt the formalism developed in [69,70,71,72,73], and follow the notation of [73]. The equations of motion satisfied by the background scalars, in which we assume that the profiles Φa(r) depend only on the radial direction, are the following:. The equations of motion for the gauge-invariant fluctuations are the following [73]: 0=. Are algebraic, we can solve them and replace into eq (2.18), which yields the general, gauge-invariant equation for the n scalar fluctuations:. The gauge-invariant fluctuations aa have a clear physical interpretation They result from the mixing of the fluctuations of the scalars φa and the trace of the four-dimensional part of the metric h. The former is connected with the (scalar) field-theory operators at the boundary, the latter with the trace of the stress-energy tensor of the boundary theory. We anticipate that in the numerical calculations we will normalise the spectra in units of the lightest tensor mode, as a way to set a universal scale in comparing between different gravity backgrounds (and dual field theories)

Applications
Example A: the Goldberger-Wise system
Example B: the GPPZ system and five-dimensional maximal supergravity
Example C: circle reduction of Romans supergravity
Example D: toroidal reduction of seven-dimensional maximal supergravity
Example E: toroidal reduction of generic AdSD backgrounds
Spectrum and connection with large-D gravity
Generalisation to other dimensions
Summary and outlook
Full Text
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