Dilaton Dynamics from Production of Tensionless Membranes

TL;DR

The paper investigates how dynamical membrane states in 11D supergravity influence dilaton and moduli evolution in a cosmological setting. By combining a tractable BPS membrane spectrum with time-dependent backgrounds, it shows generic production is Planck-suppressed, but enhanced-symmetry (tensionless) states can be produced ubiquitously and drive moduli toward duality fixed points, notably around $g_s=1$. This leads to an attractor behavior in moduli space and, with backreaction, a trapping of the dilaton and extra-dimensional radii, potentially yielding a radiation-dominated, three-large-dimensions universe at late times. The work emphasizes that UV membrane states—beyond the naive EFT—can critically shape vacuum selection and cosmological dynamics, motivating further study of strong-coupling regimes and radiative corrections. Key results hinge on the mass spectrum of BPS membranes, the non-adiabatic production near ESPs, and the backreaction-driven moduli trapping that guides the system toward duality-fixed points.

Abstract

In this paper we consider classical and quantum corrections to cosmological solutions of 11D SUGRA coming from dynamics of membrane states. We first consider the supermembrane spectrum following the approach of Russo and Tseytlin for consistent quantization. We calculate the production rate of BPS membrane bound states in a cosmological background and find that such effects are generically suppressed by the Planck scale, as expected. However, for a modified brane spectrum possessing enhanced symmetry, production can be finite and significant. We stress that this effect could not be anticipated given only a knowledge of the low-energy effective theory. Once on-shell, inclusion of these states leads to an attractive force pulling the dilaton towards a fixed point of S-duality, namely $g_s=1$. Although the SUGRA description breaks down in this regime, inclusion of the enhanced states suggests that the center of M-theory moduli space is a dynamical attractor. Morever, our results seem to suggest that string dynamics does indeed favor a vacuum near fixed points of duality.

Figures (7)

• Figure 1: The non-abiabatic parameter ${\omega^\prime}/{\omega^{2}}$ for different values of $\xi$, with $\xi=0$ (top curve), conformal coupling $\xi=9/40$ (middle curve), and $\xi=5$ (bottom curve). As $\xi$ increases, non-adiabaticity is suppressed. Note that the non-adiabticity is concentrated near $\eta \approx 0$ for all choices of $\xi$.
• Figure 2: The non-adiabatic parameter ${\omega^\prime}/{\omega^{2}}$ for different values of the flux $h=1/150$ (top curve), $h=1/100$ (middle curve), and $h=1/50$ (bottom curve).
• Figure 3: The non-adiabatic parameter ${\omega^\prime}/{\omega^{2}}$ for different values of the momentum $k_3=1/500$ (top line), $k_3=1/100$ (middle line), and $k_3=1/50$ (bottom line).
• Figure 4: Evolution of $R_{11}$ and $b$ for the exact density (\ref{['rhogo']}) and pressures, including only the membrane sources related to $R_{11}$.
• Figure 5: Evolution of $R_{11}$ (dark curve) and $b$ (light curve) for the exact density (\ref{['rhogo']}) and pressures, including membranes in all extra dimensions.