Light dilaton near critical points in top-down holography

Abstract

We study a class of UV-complete, strongly coupled, confining three-dimensional field theories, that exhibit a novel stabilisation mechanism for the mass of the lightest scalar composite state, relying on the existence of a critical point. The theories admit a holographic dual description in terms of regular backgrounds in eleven-dimensional supergravity. Their phase diagram includes a line of first-order phase transitions ending at the critical point, where the transition becomes of second order. We calculate the mass spectrum of bound states of the field theory, by considering fluctuations around the background solutions, and find that, near the critical point, a hierarchy of scales develops, such that one state becomes parametrically light. We identify this state as the dilaton, the pseudo-Nambu-Goldstone boson associated with the spontaneous breaking of approximate scale invariance. This stabilisation mechanism might be exploited to address hierarchy problems in particle and astroparticle physics.

Figures (6)

• Figure 1: Free energy density, $\mathcal{F}\ell^3$ (left panel), and response function, $\langle T_{22}\rangle \ell^3$ (right panel), as functions of the circumference, $\ell\Lambda$, of the compact dimension for confining solutions with the representative choice $b_0 = 0.6836$. The solid black disks indicate the location of a first-order phase transition between two different confining solutions. Beyond the hollow orange disk non-confining solutions are energetically favored.
• Figure 2: Phase diagram of the system. Dotted blue and solid orange curves separate confined and non-confined phases, the former identifying first-order phase transitions. Details of the region near the triple point, $b_0^{\text{\tiny triple}}\simeq 0.6847$ (black disk), are shown in the inset panel. A line of first-order phase transitions (dashed black) between different confined states joins $b_0^{\text{\tiny triple}}$ to the critical point at $b_0^{\text{\tiny CP}}\simeq 0.6815$ (white disk).
• Figure 3: Left panels: component of the stress tensor in the compact direction, $\langle T_{22}\rangle\ell^3 \alpha^{-1}$, as a function of its size, $\ell$, for representative values of $b_0$. For values of $b_0$ such that there is a first-order phase transition we define $\ell_0$ as the value of $\ell$ at the phase transition. When there is no transition, we instead define $\ell_0$ as the value of $\ell$ for which $\langle T_{22} \rangle \ell^3 \alpha^{-1}$ is the steepest. The range of parameters plotted is chosen to cluster around the line of first-order phase transitions denoted by black dashed lines in Fig. \ref{['fig_free_energy_and_T22']}. Right column: mass spectrum of scalar fluctuations, $m$, in units of the lightest vector mass, $m_0$, in the backgrounds of the left panels.
• Figure 4: Response function, $\langle T_{22}\rangle\ell^3 \alpha^{-1}$ (left), and scalar spectrum (right) for a value of $b_0<b_0^{\text{\tiny CP}}$ chosen well below the critical point. Large values of $\ell \Lambda$ approach the boundary between confining and non-confining configurations.
• Figure 5: Response functions, $\langle T_{22}\rangle\ell^3 \alpha^{-1}$ (left), and scalar spectrum (right) for values of $b_0>b_0^{\text{\tiny CP}}$, so that a first-order phase transition appears. The top row shows a representative case well above the critical point, where the first-order phase transition is between confining and non-confining solutions. In the bottom row $b_0\simeq b_0^{\text{\tiny triple}}$, slightly below the triple point.