New Geometric Approaches to Finite Temperature String Theory

Abstract

In quantum field theory a system at finite temperature can equivalently be viewed as having a compactified dimension. This situation carries over into string theory and leads to thermal duality, which relates the physics of closed strings at temperature T to the physics at the inverse temperature 1/T. Unfortunately, the classical definitions of thermodynamic quantities such as entropy and specific heat are not invariant under the thermal duality symmetry. We shall therefore pursue two different approaches. We shall investigate whether there might nevertheless exist special solutions for the string effective potential such that the duality symmetry will be preserved for all thermodynamic quantities. Imposing thermal duality covariance, we derive unique functional forms for the temperature-dependence of the string effective potentials.The second approach is to investigate self-consistent modifications to the rules of ordinary thermodynamics such that thermal duality is preserved. After all, methods of calculation should not break fundamental symmetries. We therefore propose a modification of the traditional definitions of these quantities, yielding a manifestly duality-covariant thermodynamics. At low temperatures, these modifications produce "corrections" to the standard definitions of entropy and specific heat which are suppressed by powers of the string scale. These corrections may nevertheless be important for the full development of a consistent string thermodynamics.One can also investigate the limitations of this geometric interpretation of temperature. Until recently, it appeared as though the temperature/geometry equivalence held in all string theories, but it appears to be broken for the heterotic string. We shall show this breaking by considering the SO(32) heterotic string in ten dimensions.The breaking of the geometric/finite temperature correspondence in the context of the heterotic string, leads to two different philosophical approaches when examining string systems at finite temperature. One approach is to discard the geometrical interpretation of temperature and ignore the string consistency conditions to follow the standard rules of statistical mechanics. This approach does not seem to lead to self-consistent string models. The second approach is to take the string consistency conditions as fundamental and explore their implications for systems at finite temperature. We shall examine some of the consequences of this approach.