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arXiv · hep-th/0205014

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

Michele Maggiore
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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 $F(T)\sim ΛT^2$, where $Λ$ 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.

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Michele Maggiore. 2002-05-01. The Atick-Witten free energy, closed tachyon condensation and deformed Poincare' symmetry. https://doi.org/10.1016/s0550-3213(02)00938-0

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