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August 2004 The Hagedorn/Deconfinement Phase Transition in Weakly CoupledLarge N Gauge Theories
Ofer Aharony, Joseph Marsano, Shiraz Minwalla, Kyriakos Papadodimas, Mark Van Raamsdonk
Adv. Theor. Math. Phys. 8(4): 603-696 (August 2004).


We demonstrate that weakly coupled, large $N, d$-dimensional $SU(N)$ gauge theories on a class of compact spatial manifolds (including $S^{d-1}\times {\rm time}$) undergo deconfinement phase transitions at temperatures proportional to the inverse length scale of the manifold in question. The low temperature phase has a free energy of order one, and is characterized by a stringy (Hagedorn) growth in its density of states. The high temperature phase has a free energy of order $N^2$. These phases are separated either by a single first order transition that generically occurs below the Hagedorn temperature or by two continuous phase transitions, the first of which occurs at the Hagedorn temperature. These phase transitions could perhaps be continuously connected to the usual flat space deconfinement transition in the case of confining gauge theories, and to the Hawking-Page nucleation of $AdS_5$ black holes in the case of the $\mathcal{N}=4$ supersymmetric Yang-Mills theory. We suggest that deconfinement transitions may generally be interpreted in terms of black hole formation in a dual string theory. Our analysis proceeds by first reducing the Yang-Mills partition function to a $(0+0)$-dimensional integral over a unitary matrix $U$, which is the holonomy (Wilson loop) of the gauge field around the thermal time circle in Euclidean space; deconfinement transitions are large $N$ transitions in this matrix integral.


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Ofer Aharony. Joseph Marsano. Shiraz Minwalla. Kyriakos Papadodimas. Mark Van Raamsdonk. "The Hagedorn/Deconfinement Phase Transition in Weakly CoupledLarge N Gauge Theories." Adv. Theor. Math. Phys. 8 (4) 603 - 696, August 2004.


Published: August 2004
First available in Project Euclid: 2 June 2005

zbMATH: 1079.81046
MathSciNet: MR2141498

Rights: Copyright © 2004 International Press of Boston


Vol.8 • No. 4 • August 2004
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