论文标题
弦理论中的热平衡
Thermal Equilibrium in String Theory in the Hagedorn Phase
论文作者
论文摘要
在弦理论中，固定周长的热圆$ s^{1}_β$在热状态下描述了热状态。但是，该周长是一个动态场，可能在空间上有所不同，因此不能保证热平衡。我们讨论了在Hagedorn温度附近和之上的II型弦理论的热状态，并表明在存在均匀的各向同性通量的情况下，热圆的周长确实可以固定和稳定。我们求解了从重现树级字符串S-matrix的动作的运动方程。我们在固定温度下找到了$ s^{1}_β\ times s^2 \ times s^2 \ times s^2 \ times s^2 \ times s^2 \ times s^{d-2} $的解决方案，其中包括$ s^1__p^2 $ s^2 $ s^2 $ s^2 $ s^2 $ s^2 $。我们发现的溶液具有线性diLATON或恒定的dilaton，在这种情况下，我们发现具有宇宙常数或Ramond-Ramond通量的溶液。然后，我们将解决方案与与$ SL（2，r）/u（1）$ cOSET理论相关的雪茄和气缸背景进行了比较，该理论包括绕组模式冷凝物但没有通量。我们还将解决方案与不均匀的Horowitz-Polchinski溶液进行比较，该溶液还具有绕组模式冷凝物，其特征是在Hagedorn温度附近具有近似的热平衡。
In string theory, a thermal state is described by compactifying Euclidean time on a thermal circle $S^{1}_β$, of fixed circumference. However, this circumference is a dynamical field which could vary in space, therefore thermal equilibrium is not guaranteed. We discuss a thermal state of type II string theory near and above the Hagedorn temperature and show that the circumference of the thermal circle can indeed be fixed and stabilized in the presence of a uniform isotropic flux. We solve the equations of motion derived from an action that reproduces the tree-level string S-matrix. We find solutions with the topologies of $S^{1}_β\times S^2 \times {\cal M}^{d-2}$ at a fixed temperature, which include a space-filling winding-mode condensate and a uniform Neveu-Schwarz Neveu-Schwarz flux supported on $S^1_β\times S^2$. The solutions that we find have either a linear dilaton or a constant dilaton, in which case, we find solutions with either a cosmological constant or a Ramond-Ramond flux. We then compare our solutions to the cigar and cylinder backgrounds associated with the $SL(2,R)/U(1)$ coset theory, which include a winding-mode condensate but without flux. We also compare and contrast our solutions with the non-uniform Horowitz-Polchinski solution, which also possesses a winding-mode condensate and is characterized by an approximate thermal equilibrium near the Hagedorn temperature.
