# Examples of spontaneously broken scale invariance?

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To me it is intuitively clear, how scale invariance of a theory can explicitely be broken by adding terms into the Lagrangian that introduce an explicit scale, such as a mass term for example. Conversely, how it can happen that scale invariance is spontaneously broken is intuitively less clear to me...

So can anybody give some enlightening examples such that I can explicitely see what kind of mechanism esxist that spontaneously break scale invariance and how this works exactly?

edited May 19, 2014

Just from reading the abstract (didn't read the full text), maybe this and this are examples.

One of the simplest example of scale invariant theory is N=4 Super-Yang-Mills in four dimensions. This is a scale (in fact conformal) invariant gauge theory. There are 6 scalars in the adjoint representation of the gauge group and the expectation values of these scalars define a moduli space $M = \mathbb{R}^{6}$, called the Coulomb branch. At the origin, no scalar expectation value, unbroken gauge group, scale invariance. At a generic point, some scalar expectation values, broken gauge group by Higgs mechanism and broken scale invariance: some particles are massive.
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