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

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Summary

Introduction

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

Random walks in AdS3
General analysis of α corrections
Atick-Witten tachyon
Type II superstring in AdS3 space
Summary
Euclidean BTZ model
Thermal tachyons
Cylinder-winding tachyons
AdS3 orbifolds: conical spaces
Thermal spectrum
Numerical analysis
Dominant state
Hagedorn temperature
Dominant state and critical Hagedorn thermodynamics
The AdS3 field theory point of view
Winding states from the field theory action
Exact WZW analysis for non-winding states
Thermal scalar action
Flat space limit
Random walk behavior in AdS3
Cigar-winding states
Conclusions and outlook
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