Quantum stabilization of thermal brane-worlds in M-theory

Low-energy effective M-theory (11d supergravity or 11d SUSY theory) is considered in 11d flat or AdS background. After orbifold compactification of eleventh dimension one gets flat 10d brane at non-zero temperature. Quantum effective potential (free energy at low-temperature approximation) is calculated on such brane with account of only lowest mass from Kaluza–Klein modes. Such effective potential may stabilize the radius of 11th dimension (radion stabilization) as it is demonstrated explicitly.