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LARGE Volume String Compactifications at Finite Temperature

Lilia Anguelova, Vincenzo Calo, Michele Cicoli

Abstract

We present a detailed study of the finite-temperature behaviour of the LARGE Volume type IIB flux compactifications. We show that certain moduli can thermalise at high temperatures. Despite that, their contribution to the finite-temperature effective potential is always negligible and the latter has a runaway behaviour. We compute the maximal temperature $T_{max}$, above which the internal space decompactifies, as well as the temperature $T_*$, that is reached after the decay of the heaviest moduli. The natural constraint $T_*<T_{max}$ implies a lower bound on the allowed values of the internal volume $\mathcal{V}$. We find that this restriction rules out a significant range of values corresponding to smaller volumes of the order $\mathcal{V}\sim 10^{4}l_s^6$, which lead to standard GUT theories. Instead, the bound favours values of the order $\mathcal{V}\sim 10^{15}l_s^6$, which lead to TeV scale SUSY desirable for solving the hierarchy problem. Moreover, our result favours low-energy inflationary scenarios with density perturbations generated by a field, which is not the inflaton. In such a scenario, one could achieve both inflation and TeV-scale SUSY, although gravity waves would not be observable. Finally, we pose a two-fold challenge for the solution of the cosmological moduli problem. First, we show that the heavy moduli decay before they can begin to dominate the energy density of the Universe. Hence they are not able to dilute any unwanted relics. And second, we argue that, in order to obtain thermal inflation in the closed string moduli sector, one needs to go beyond the present EFT description.

LARGE Volume String Compactifications at Finite Temperature

Abstract

We present a detailed study of the finite-temperature behaviour of the LARGE Volume type IIB flux compactifications. We show that certain moduli can thermalise at high temperatures. Despite that, their contribution to the finite-temperature effective potential is always negligible and the latter has a runaway behaviour. We compute the maximal temperature , above which the internal space decompactifies, as well as the temperature , that is reached after the decay of the heaviest moduli. The natural constraint implies a lower bound on the allowed values of the internal volume . We find that this restriction rules out a significant range of values corresponding to smaller volumes of the order , which lead to standard GUT theories. Instead, the bound favours values of the order , which lead to TeV scale SUSY desirable for solving the hierarchy problem. Moreover, our result favours low-energy inflationary scenarios with density perturbations generated by a field, which is not the inflaton. In such a scenario, one could achieve both inflation and TeV-scale SUSY, although gravity waves would not be observable. Finally, we pose a two-fold challenge for the solution of the cosmological moduli problem. First, we show that the heavy moduli decay before they can begin to dominate the energy density of the Universe. Hence they are not able to dilute any unwanted relics. And second, we argue that, in order to obtain thermal inflation in the closed string moduli sector, one needs to go beyond the present EFT description.

Paper Structure

This paper contains 36 sections, 182 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Large Volume Scenarios
  3. Type IIB with fluxes
  4. Leading order corrections
  5. Non-perturbative corrections
  6. $\alpha'$ corrections
  7. $g_s$ corrections
  8. Moduli stabilisation in LVS
  9. Swiss-cheese Calabi-Yaus
  10. Fibred Calabi-Yaus
  11. Effective potential at finite temperature
  12. General form of temperature corrections
  13. Thermal equilibrium
  14. $2\leftrightarrow 2$ interactions
  15. $1\leftrightarrow2$ interactions
  16. ...and 21 more sections

Figures (3)

  • Figure 1: The effective potential $V$ versus the volume modulus $\phi$ for a typical potential of KKLT or LARGE Volume compactifications. The different curves show the effect of various sources of energy that, if higher than the barrier of the potential, can lead to a decompactification of the internal space.
  • Figure 4: Scattering process $\Phi g\rightarrow g g$ through which the modulus $\Phi$ and gluons can reach thermal equilibrium.
  • Figure 5: Plot of the $R=1$ curve in the ($x$,$c$)-plane. The shaded region represents the phenomenologically forbidden area, in which the values of $x$ and $c$ are such that $R<1$$\Leftrightarrow$$T_{max}<T_*$.