标量QFT中的膨胀：$4-\varepsilon$和$3-\varepsilon$维中的不可行定理
Dilaton in scalar QFT: a no-go theorem in $4-\varepsilon$ and $3-\varepsilon$ dimensions
摘要：
在$4-\varepsilon$维的可重整化、幺正、相互作用非超对称标量场理论中研究了自发标度不变性破缺和相应的Goldstone玻色子。在首阶，我们可以构造一些模型，使标度不变性自发地经典地破缺，并且确实可以识别出一个无质量的量子。在首阶之外，为了避免QFT中的反常标度对称破缺，需要将模型定义在具有精确共形对称的Wilson-Fisher不动点上。它表明，这一要求的耦合是不兼容的类型的平面方向，这将是必要的一个完全无质量的椭圆形。结果表明，在可重整化的$4-\varepsilon$维标量QFT中，不可能出现自发的标度对称破缺和精确无质量的量子。这些论证也适用于$3-\varepsilon$维的$ϕ^6$理论。
英文摘要：
Spontaneous scale invariance breaking and the associated Goldstone boson, the dilaton, is investigated in renormalizable, unitary, interacting non-supersymmetric scalar field theories in $4-\varepsilon$ dimensions. At leading order it is possible to construct models which give rise to spontaneous scale invariance breaking classically and indeed a massless dilaton can be identified. Beyond leading order, in order to have no anomalous scale symmetry breaking in QFT, the models need to be defined at a Wilson-Fisher fixed point with exact conformal symmetry. It is shown that this requirement on the couplings is incompatible with having the type of flat direction which would be necessary for an exactly massless dilaton. As a result spontaneous scale symmetry breaking and an exactly massless dilaton can not occur in renormalizable, unitary $4-\varepsilon$ dimensional scalar QFT. The arguments apply to $ϕ^6$ theory in $3-\varepsilon$ dimensions as well.
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