# Examples of spontaneously broken scale invariance?

+ 3 like - 0 dislike
2505 views

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.
 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:$\varnothing\hbar$ysicsOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). Please complete the anti-spam verification