Anomalies, conformal manifolds, and spheres
Anomalies, conformal manifolds, and spheres
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异常、共形流形和球体
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
S. Theisen
中科院分区：
文献类型：
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作者：
J. Gomis;Po;Z. Komargodski;A. Schwimmer;N. Seiberg;S. Theisen
精确边缘算子的两点函数导致了偶数维迹异常的普遍贡献。我们研究了这种道异常的一些方面，强调它的解释是一个西格玛模型，它的目标空间ℳ$$\mathm{\mathcal{\数学{M}}$$是保形场论的空间(又名。共形流形)。当基本的量子场论是超对称的时，这个西格玛模型必须适当地超对称。作为例子，我们较详细地考虑了d=2中N=2，2$$\数学{N}=左(2，2\右)$和N=0，2$$\数学{N}=左(0，2\右)$$超对称理论，并进一步证明了d=4中超对称理论的Kähler-Hodge类是零的。对于d=2中的N=2，2$$\数学{N}=左(2，2\右)$$理论和d=4中的N=2$$\数学{N}=2$$理论，我们还证明了球面配分函数与ℳ$$\mathcal{数学{M}}$的Kähler势之间的关系直接源于我们所构造的适当的sigma模型.在此过程中，我们发现了几个符合Wess-Zumino一致性条件的潜在踪迹异常的例子，但可以通过更详细的分析来排除。
A bstractThe two-point function of exactly marginal operators leads to a universal contribution to the trace anomaly in even dimensions. We study aspects of this trace anomaly, emphasizing its interpretation as a sigma model, whose target space ℳ$$ \mathrm{\mathcal{M}} $$ is the space of conformal field theories (a.k.a. the conformal manifold). When the underlying quantum field theory is supersymmetric, this sigma model has to be appropriately supersymmetrized. As examples, we consider in some detail N=2,2$$ \mathcal{N}=\left(2,\;2\right) $$ and N=0,2$$ \mathcal{N}=\left(0,\;2\right) $$ supersymmetric theories in d = 2 and N=2$$ \mathcal{N}=2 $$ supersymmetric theories in d = 4. This reasoning leads to new information about the conformal manifolds of these theories, for example, we show that the manifold is Kähler-Hodge and we further argue that it has vanishing Kähler class. For N=2,2$$ \mathcal{N}=\left(2,\;2\right) $$ theories in d = 2 and N=2$$ \mathcal{N}=2 $$ theories in d = 4 we also show that the relation between the sphere partition function and the Kähler potential of ℳ$$ \mathrm{\mathcal{M}} $$ follows immediately from the appropriate sigma models that we construct. Along the way we find several examples of potential trace anomalies that obey the Wess-Zumino consistency conditions, but can be ruled out by a more detailed analysis.
影响因子：
5.4
作者：
J. Gomis;Sungjay Lee
通讯作者：
J. Gomis;Sungjay Lee