Abstract
We analyze near-Hagedorn thermodynamics of strings in the WZW $AdS_3$ model. We compute the thermal spectrum of all primaries and find the thermal scalar explicitly in the string spectrum using CFT twist techniques. Then we use the link to the Euclidean WZW BTZ black hole and write down the Euclidean BTZ spectrum. We give a Hamiltonian interpretation of the thermal partition function of angular orbifolds where we find a reappearance of discrete states that dominate the partition function. Using these results, we discuss the nature of the thermal scalar in the WZW BTZ model. As a slight generalization of the angular orbifolds, we discuss the $AdS_3$ string gas with a non-zero chemical potential corresponding to angular momentum around the spatial cigar. For this model as well, we determine the thermal spectrum and the Hagedorn temperature as a function of chemical potential. Finally the nature of $\alpha'$ corrections to the $AdS_3$ thermal scalar action is analyzed and we find the random walk behavior of highly excited strings in this particular $AdS_3$ background.
Highlights
String theory models on WZW AdS3 and BTZ have been fruitful toy models to study string dynamics on non-trivial target spaces
We have discussed thermal properties of the AdS3 and BTZ WZW models from the thermal spectrum
We explicitly found the thermal scalar in the string spectrum with the correct mass
Summary
String theory models on WZW AdS3 and BTZ have been fruitful toy models to study string dynamics on non-trivial target spaces. An equivalent way of thinking about this is through the thermal scalar This string state is in the perturbative spectrum on the thermal manifold and captures the critical thermodynamics at temperatures sufficiently close to the Hagedorn temperature. There we have given a path integral picture of the thermal scalar in general curved backgrounds (following the derivation of [26]). This reduces the string path integral to a particle path integral given by: Zp = 2 This realizes the random walk picture of the thermal scalar directly in the path integral language. There are corrections to the above particle action We saw that these can be deduced from the field theory of the thermal scalar. Determine the complete random walk picture of a highly excited string gas in these spacetimes. We present background material on WZW models and more elaborate calculations in the appendices
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