The AtickWitten free energy, closed tachyon condensation and deformed Poincaré symmetry
Abstract
The dependence of the free energy of string theory on the temperature at T≫ T_{Hag} was found long ago by Atick and Witten and is F( T)∼ ΛT^{2}, 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 noncommutative 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 worldsheet. This result indicates that the endpoint of the condensation of closed string tachyons with nonzero winding is an infinite stack of spacelike branes with a given noncommutative worldvolume geometry. On a more technical side, we also point out that Tduality along a circle with antiperiodic boundary conditions for spacetime fermions is broken by worldsheet vortices, and the wouldbe Tdual variable becomes noncompact.
 Publication:

Nuclear Physics B
 Pub Date:
 December 2002
 DOI:
 10.1016/S05503213(02)009380
 arXiv:
 arXiv:hepth/0205014
 Bibcode:
 2002NuPhB.647...69M
 Keywords:

 High Energy Physics  Theory
 EPrint:
 31 pages, 3 figures