Non-perturbative aspects of gauge theories from gauge-gravity dualities

Abstract

We consider two established supergravities which are known to provide the low-energy effective description of either superstring theory or M-theory: the six-dimensional theory of Romans, and the maximal supergravity in seven dimensions. We compactify on an $S^{1}$ and $T^{2}$, respectively, to obtain 5D sigma-models coupled to gravity, and spectra of bosonic excitations are computed numerically by fluctuating fields on backgrounds which holographically realise confinement. We propose a method to detect mixing effects between scalar resonances and the pseudo-Nambu--Goldstone boson associated with spontaneous breaking of conformal invariance: the dilaton. This test consists of neglecting a key component of the spin-0 fluctuation variables, effectively disregarding their back-reaction on the underlying geometry; where discrepancies arise compared to the proper calculation we infer dilaton mixing. In both cases this analysis evinces a parametrically light dilaton. For each theory we also uncover a tachyonic instability within their parameter space. We hence proceed to investigate their respective phase structures, reasoning that some mechanism must render the instabilities physically inaccessible. We compile a catalogue of geometrically distinct backgrounds within each theory, and derive general expressions for their holographically renormalised free energy $F$. Another numerical routine is used to systematically extract data for some special deformation parameters, and $F$ is plotted in units of an appropriate universal scale. Our analysis proves fruitful: each theory shows evidence of a first-order phase transition which induces the spontaneous decompactification of the shrinking dimension before the instability manifests, favouring instead a branch of singular solutions. The light dilaton resonance appears only along a metastable portion of the branch of confining backgrounds.