Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-01-19
Nucl.Phys. B602 (2001) 109-131
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, 2 figures, harvmac. References added, final version to appear in Nucl.Phys.B
Scientific paper
10.1016/S0550-3213(01)00128-6
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_{\rm cr} \cong 0.31 l_P^ {-1} $ (so it is very small in string units).
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