Hagedorn divergences and tachyon potential

Abstract

We consider the critical behavior for a string theory near the Hagedorn temperature. We use the factorization of the worldsheet to isolate the Hagedorn divergences at all genera. We show that the Hagedorn divergences can be resummed by introducing double scaling limits, which smooth the divergences. The double scaling limits also allow one to extract the effective potential for the thermal scalar. For a string theory in an asymptotic anti-de Sitter (AdS) spacetime, the AdS/CFT correspondence implies that the critical Hagedorn behavior and the relation with the effective potential should also arise from the boundary Yang-Mills theory. We show that this is indeed the case. In particular we find that the free energy of a Yang-Mills theory contains ``vortex'' contributions at finite temperature. Yang-Mills Feynman diagrams with vortices can be identified with contributions from boundaries of moduli space on the string theory side.

36 pages, 13 figures, uses harvmac

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• Random Walks in Rindler Spacetime and String Theory at the Tip of the Cigar
• Confinement/Deconfinement Transition of Large N Gauge Theories in Perturbation Theory with N_f Fundamentals: N_f/N Finite
• Hagedorn Strings and Correspondence Principle in AdS(3)
• The Buchdahl Stability Bound in Eddington-inspired Born-Infeld Gravity
• Hagedorn String Thermodynamics in Curved Spacetimes and near Black Hole Horizons