Dilaton Destabilization at High Temperature

TL;DR

The paper demonstrates that finite-temperature effects induce a negative linear term in the dilaton potential, creating a critical temperature $T_{\rm crit}$ above which the stabilized vacuum collapses and all moduli destabilize. By analyzing racetrack and Kähler stabilization scenarios, it derives $T_{\rm crit}$ as a function of SUSY-breaking scales, gaugino-condensation parameters, and the Kähler geometry, finding typical values around $10^{11}$–$10^{12}$ GeV. This imposes a universal upper bound on the reheating temperature and radiation-dominated era of the early universe, with significant implications for baryogenesis, leptogenesis, and inflation model-building, and it cannot be avoided by late-time entropy production. The work highlights a robust cosmological constraint tied to the dilaton dynamics in weakly coupled heterotic-like theories and motivates further study in more general compactifications.

Abstract

Many compactifications of higher-dimensional supersymmetric theories have approximate vacuum degeneracy. The associated moduli fields are stabilized by non-perturbative effects which break supersymmetry. We show that at finite temperature the effective potential of the dilaton acquires a negative linear term. This destabilizes all moduli fields at sufficiently high temperature. We compute the corresponding critical temperature which is determined by the scale of supersymmetry breaking, the beta-function associated with gaugino condensation and the curvature of the K"ahler potential, T_crit ~ (m_3/2 M_P)^(1/2) (3/β)^(3/4) (K'')^(-1/4). For realistic models we find T_crit ~ 10^11-10^12 GeV, which provides an upper bound on the temperature of the early universe. In contrast to other cosmological constraints, this upper bound cannot be circumvented by late-time entropy production.

Figures (6)

• Figure 1: The coefficient $B$ (cf. Eq. \ref{['omega']}) for $\mathrm{SU}(N_c)$ gauge theory with $N_f$ flavours; $g_0 = 1/\sqrt{2}$.
• Figure 2: Typical potential for dilaton stabilization (solid curve). A minimum at $S=S_\mathrm{min}\simeq2$ is separated from the other minimum at $S\to \infty$ by a finite barrier. For illustration, we also plot a typical run--away potential (dashed curve).
• Figure 3: Dilaton potential for $(N_1,N_2)=(7,8)$ and $(M_1,M_2)=(8,15)$. (a): $T=0$, (b): $T=T_\mathrm{crit}$. In (b) the dilaton independent term $A\, T_\mathrm{crit}^4$ has been subtracted (cf. Eq. \ref{['linear']}).
• Figure 4: Dilaton potential for Kähler stabilization. $c=5.7391$, $p=1.1$, $q=1$, and $N=6$Barreiro:1997rp. (a): $T=0$, (b): $T=T_\mathrm{crit}$. In (b) the dilaton independent term $A\, T_\mathrm{crit}^4$ has been subtracted (cf. Eq. \ref{['linear']}).
• Figure 5: Three epochs in inflationary models: inflation, inflaton oscillation domination and radiation domination Kolb-Turner.