Free energy and critical temperature in eleven dimensions

Abstract

We compute the one-loop contribution to the free energy in eleven-dimensional supergravity, with the eleventh dimension compactified on a circle of radius $R_{11}$. We find a finite result, which, in a small radius expansion, has the form of the type IIA supergravity free energy plus non-perturbative corrections in the string coupling $g_A$, whose coefficients we determine. We then study type IIA superstring theory at finite temperature in the strong coupling regime by considering M-theory on $R^9\times T^2$, one of the sides of the torus being the euclidean time direction, where fermions obey antiperiodic boundary conditions. We find that a certain winding membrane state becomes tachyonic above some critical temperature, which depends on $g_A$. At weak coupling, it coincides with the Hagedorn temperature, at large coupling it becomes $T_{\mathrm{cr}}\cong 0.31l_P^{-1}$ (so it is very small in string units).

24 pages, 2 figures, harvmac. References added, final version to appear in Nucl.Phys.B

Cited by in corpus (9)

• Magnetic backgrounds and tachyonic instabilities in closed superstring theory and M-theory
• Brane gases in the early universe: thermodynamics and cosmology
• Strings at Finite Temperature: Wilson Lines, Free Energies, and the Thermal Landscape
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
• Hagedorn String Thermodynamics in Curved Spacetimes and near Black Hole Horizons
• Re-Identifying the Hagedorn Transition
• Quantum State Density and Critical Temperature in M-theory
• Quantum States, Thermodynamic Limits and Entropy in M-Theory
• Holographic Hagedorn Temperature: Strong Coupling, Flavor and $\theta$-angle Effects