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arXiv 2004.05223hep-th
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弦论模型的半经典分析

Semi-Classical Analysis of the String Theory Cigar

Daniel Louis Jafferis, Elliot Schneider

摘要:

研究了SL(2,R)_k/U(1)CFT的反射系数的半经典极限。对于大的k,CFT描述了一个在具有2维强子引力的欧几里得黑洞中的弦,其目标空间是一根具有渐近线性强子的雪茄。这种西格玛模型的描述是弱耦合在大k极限,我们调查的鞍点展开的功能积分计算反射系数。在半经典极限的刘维尔CFT,我们发现,必须复化的功能积分和总和复杂的鞍重现的限制,确切的反射系数。与Liouville不同,SL(2,R)_k/U(1)CFT允许以反射系数极点形式出现的束缚态.为了在半经典极限下再现它们,我们发现必须对击中黑洞奇点的配置求和,但仍然对具有有限作用的鞍点膨胀有贡献。

英文摘要:

We study the semi-classical limit of the reflection coefficient for the SL(2,R)_k/U(1) CFT. For large k, the CFT describes a string in a Euclidean black hole of 2-dimensional dilaton-gravity, whose target space is a cigar with an asymptotically linear dilaton. This sigma-model description is weakly coupled in the large k limit, and we investigate the saddle-point expansion of the functional integral that computes the reflection coefficient. As in the semi-classical limit of Liouville CFT, we find that one must complexify the functional integral and sum over complex saddles to reproduce the limit of the exact reflection coefficient. Unlike Liouville, the SL(2,R)_k/U(1) CFT admits bound states that manifest as poles of the reflection coefficient. To reproduce them in the semi-classical limit, we find that one must sum over configurations that hit the black hole singularity, but nevertheless contribute to the saddle-point expansion with finite action.

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