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arXiv 0908.0878hep-th
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复射影超空间上的西格玛模型

The Sigma Model on Complex Projective Superspaces

Constantin Candu, Vladimir Mitev, Thomas Quella, Hubert Saleur, Volker Schomerus

备注：
59 pages, 6 figures, 1 table
发表信息：
JHEP 1002:015,2010
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摘要：

复射影超空间CP^{S-1}上的西格玛模型|S}给出了一个连续族的相互作用的二维共形场论，它们由曲率半径R和θ角θ参数化。我们的主要目标是确定该模型的频谱，非微扰作为两个参数的函数。我们成功地做到这一点，所有开放的边界条件，保持完整的全球对称性的模型。在弦论的客厅里，这些对应于体积填充的膜，它们配备了一个双线丛和联络。论文由两部分组成。在第一部分中，我们将在连续统公式中处理这个问题。结合微扰研究和一些简单的自由场计算的组合参数，我们确定了一个封闭的配分函数的理论公式。然后在第二部分中用数字进行测试。在那里，我们提出了CP^{S-1| S}模型，并用它来确定共形不动点处的谱。数值结果与连续介质分析结果吻合得很好。

英文摘要：

The sigma model on complex projective superspaces CP^{S-1|S} gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle θ. Our main goal is to determine the spectrum of the model, non-perturbatively as a function of both parameters. We succeed to do so for all open boundary conditions preserving the full global symmetry of the model. In string theory parlor, these correspond to volume filling branes that are equipped with a monopole line bundle and connection. The paper consists of two parts. In the first part, we approach the problem within the continuum formulation. Combining combinatorial arguments with perturbative studies and some simple free field calculations, we determine a closed formula for the partition function of the theory. This is then tested numerically in the second part. There we propose a spin chain regularization of the CP^{S-1|S} model with open boundary conditions and use it to determine the spectrum at the conformal fixed point. The numerical results are in remarkable agreement with the continuum analysis.

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