Difference between instantons and sphalerons What is the difference between instantons and sphalerons? If they are different, how do they violate baryon and lepton number in the standard electroweak theory? 
 A: The sphaleron is kind of the opposite of the instanton, and kind of the same. Let's make that statement precise:
An instanton is a local minimum of the action that mediates vacuum tunneling (link to an answer of mine how and why instantons do that). The sphaleron sits in-between the vacua, in a certain sense, it is the instanton "in the middle of tunneling":
Given an instanton configuration $A_\text{inst}$ on a 4-cylinder $(-\infty,\infty) \times S^3$, representing tunneling between two vacua at the spatial slices at $t = \pm \infty$ with Chern-Simons winding numbers differing by 1, the sphaleron is vaguely the field configuration $A(t = 0)$, and precisely the field configuration for which, at some time $t_0$, the winding number as the integral of the Chern-Simons form
$$ \int_{{t_0} \times S^3}\omega \equiv \int_{{t_0} \times S^3} \mathrm{tr}(F\wedge A - \frac{1}{3}A \wedge A \wedge A) $$
is exactly the mean of the winding numbers of the vacua at the ends.
The idea is that an instanton of winding number 1 mediates between vacua of winding numbers $k$ and $k+1$, and that the sphaleron is the field configuration "in the middle", with winding number $\frac{2k+1}{2}$. The reason this is interesting is because, for example, in the electroweak theory, the bosonic potential part of the action is (of course) minimal for the vacuum/instanton configurations, and maximal for the sphaleron configuration. That's why the sphaleron is called that (it's Greek for slippery thing) - it may slip down into either vacuum configuration because it is sitting in a metastable extremum of the potential.
