The Atick-Witten free energy, closed tachyon condensation and deformed Poincare' symmetry

Abstract

The dependence of the free energy of string theory on the temperature at T much larger than the Hagedorn temperature was found long ago by Atick and Witten and is $F(T)\sim \Lambda T^2$, where $\Lambda$ diverges because of a tachyonic instability. We show that this result can be understood assuming that, above the Hagedorn transition, Poincare' symmetry is deformed into a quantum algebra. Physically this quantum algebra describes a non-commutative spatial geometry and a discrete euclidean time. We then show that in string theory this deformed Poincare' symmetry indeed emerges above the Hagedorn temperature from the condensation of vortices on the world-sheet. This result indicates that the endpoint of the condensation of closed string tachyons with non-zero winding is an infinite stack of spacelike branes with a given non-commutative world-volume geometry. On a more technical side, we also point out that $T$-duality along a circle with antiperiodic boundary conditions for spacetime fermions is broken by world-sheet vortices, and the would-be T-dual variable becomes non-compact.

31 pages, 3 figures

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• (De)Constructing Dimensions
• Don't Panic! Closed String Tachyons in ALE Spacetimes
• Fluxbranes in String Theory
• Some Consequences of the Generalised Uncertainty Principle: Statistical Mechanical, Cosmological, and Varying Speed of Light
• The Kaluza-Klein Melvin Solution in M-theory
• Closed String Tachyon Condensation on Twisted Circles
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