论文标题
非线性sigma模型中比例不变性的保形不变性
Conformal invariance from scale invariance in non-linear sigma models
论文作者
论文摘要
存在某种论点，即在维度上，比例不变量子场理论都是保形不变的。我们可能会尝试以$ 2N +ε$尺寸扩展该参数，但是幼稚的扩展具有一个小的漏洞，这确实显示了$ 2 +ε$尺寸的非线性Sigma模型的阻塞。即使由于漏洞而可能失败，但我们表明，比例不变性确实意味着佩雷尔曼（Perelman）在RICCI流的开创性工作中，非线性Sigma模型在$ 2+ε$维度中的形式不变性。
There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + ε$ dimensions, but the naive extension has a small loophole, which indeed shows an obstruction in non-linear sigma models in $2+ε$ dimensions. Even though it could have failed due to the loophole, we show that scale invariance does imply conformal invariance of non-linear sigma models in $2+ε$ dimension from the seminal work by Perelman on the Ricci flow.
