Abstract
We discuss near-Hagedorn string thermodynamics in general spacetimes using the formalism of the thermal scalar. Building upon earlier work by Horowitz and Polchinski, we relate several properties of the thermal scalar field theory (i.e. the stress tensor and U(1) charge) to properties of the highly excited or near-Hagedorn string gas. We apply the formulas on several examples. We find the pressureless near-Hagedorn string gas in flat space and a non-vanishing (angular) string charge in $AdS_3$. We also find the thermal stress tensor for the highly excited string gas in Rindler space.
Highlights
These results show that thermodynamical quantities such as the free energy and the entropy can be rewritten in terms of the thermal scalar
This is not the procedure we are interested in here: we are discussing the process of letting m go to zero and looking at the non-analytic behavior in m during this procedure. All of this is related to the fact that, as was discussed in subsection 2.2, we only focus on the lowest eigenmode of the thermal scalar and not on the full scalar field theory to obtain the most dominant contribution to string thermodynamics in the Hagedorn regime
The thermal scalar energy-momentum tensor captures the energy-momentum tensor of an average of highly excited Lorentzian strings
Summary
In [4], the authors consider long strings with self-interactions. This study was further analyzed in [5]. As a byproduct in their calculations, they obtain an expression for the energy-averaged stress tensor in terms of the thermal scalar It is this result that we will focus on in this note. This is why we shall continue fully from the spacetime (field theory) point of view to rederive the result of [4]. Instead of using the worldsheet non-linear sigma model (as in equation (2.1)), we focus on the spacetime action of all string modes: the string field theory action. We restrict this action to the sum of the non-interacting parts of the different string states, let us call the resulting action Se
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