Black hole/string transition for the small Schwarzschild black hole of AdS5× S5 and critical unitary matrix models
Black hole/string transition for the small Schwarzschild black hole of AdS5×
S5 and critical unitary matrix models
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AdS5× 小史瓦西黑洞的黑洞/弦过渡
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
S. Wadia
中科院分区：
文献类型：
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作者：
L. Alvarez;Pallab Basu;M. Mariño;S. Wadia
本文利用AdS/CFT对应讨论了有限温度下小史瓦西黑洞AdS5×S5的黑洞-弦跃迁。有限温度计理论在弱耦合和强耦合下的有效作用可以完全用SU(N)矩阵的恒定Polyakov线来表示。为了证明这一点，我们已经考虑到没有与10维黑洞解位于S5中的一点相关的Nambu-Goldstone模式。我们证明了规范理论中特征谱有间隙的相位对应于体理论中的超重力鞍点。我们识别了三阶N=∞相变与黑洞-弦相变。这种奇点可以在过渡区域使用双尺度极限来解决，在过渡区域中，大N展开是根据N-2/3的幂来组织的。N=∞跃迁现在变成了一个平滑的交叉，在一个重归一化的弦耦合常数方面，反映了大而有限N的物理特性。我们还讨论了我们的结果对小史瓦西黑洞洛伦兹部分奇点分辨率的影响。
In this paper we discuss the black hole–string transition of the small Schwarzschild black hole of AdS5×S5 using the AdS/CFT correspondence at finite temperature. The finite temperature gauge theory effective action, at weak and strong coupling, can be expressed entirely in terms of constant Polyakov lines which are SU(N) matrices. In showing this we have taken into account that there are no Nambu–Goldstone modes associated with the fact that the 10-dimensional black hole solution sits at a point in S5. We show that the phase of the gauge theory in which the eigenvalue spectrum has a gap corresponds to supergravity saddle points in the bulk theory. We identify the third order N=∞ phase transition with the black hole–string transition. This singularity can be resolved using a double scaling limit in the transition region where the large N expansion is organized in terms of powers of N-2/3. The N=∞ transition now becomes a smooth crossover in terms of a renormalized string coupling constant, reflecting the physics of large but finite N. Multiply wound Polyakov lines condense in the crossover region. We also discuss the implications of our results for the resolution of the singularity of the lorenztian section of the small Schwarzschild black hole.