Effect of topology on the thermodynamic limit for a string gas

Abstract

We discuss the thermodynamic limit for a gas of strings at high energy densities. This is defined by studying the statistical properties of the gas in a compact space and taking the size of the space to infinity keeping the energy density finite. We obtain a behavior that is different from earlier treatments where the gas is considered at the same energy density but living in a noncompact space. In particular we show that the gas is not dominated by a single energetic string above the Hagedorn energy density, but instead the number of energetic strings is lnR/√α' where R is the radius of the universe and α' the slope parameter. The reason for the thermodynamic behavior being sensitive to topology is the existence of winding modes that can sense the large-scale structure of the space.