The Atick-Witten free energy, closed tachyon condensation and deformed Poincaré symmetry
Abstract
The dependence of the free energy of string theory on the temperature at T≫ THag was found long ago by Atick and Witten and is F( T)∼ ΛT2, where Λ diverges because of a tachyonic instability. We show that this result can be understood assuming that, above the Hagedorn transition, Poincaré 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 Poincaré 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 space-like 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 space-time fermions is broken by world-sheet vortices, and the would-be T-dual variable becomes non-compact.
- Publication:
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Nuclear Physics B
- Pub Date:
- December 2002
- DOI:
- 10.1016/S0550-3213(02)00938-0
- arXiv:
- arXiv:hep-th/0205014
- Bibcode:
- 2002NuPhB.647...69M
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 31 pages, 3 figures