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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?

asked May 19, 2014 in Theoretical Physics by Dilaton (4,295 points) [ revision history ]
edited May 19, 2014 by dimension10

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

1 Answer

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If you take a scale invariant theory which contains some scalars then you can obtain a spontaneously broken scale invariance by giving some expectation values to the scalars. If you give some expectation values to some scalars in a gauge theory, we have the Higgs mechanism, with spontaneous breaking of the gauge symmetry. The story will be analoguous for some generic expectation values of the scalars in a scale invariant theory : at low energies, particles will obtain masses and the theory will no longer be scale invariant.

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. 

answered May 19, 2014 by 40227 (4,660 points) [ revision history ]
edited May 19, 2014 by 40227

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