In string-net condensation, what does the quantized charge mean?

Question

1. The electrical charge is quantized strictly for elementary particles. What kind ofconstraints does this fact imply when applied to string-net theory? For this question, I want to understand why electrical charges are quantized instead of having a continuous value. What part of the string-net theory quantize the charge?

2. Another question is how the end of a broken string generate a field that is almost uniform to different directions? The electron are claimed to be the end of a broken string. I imagine that at the end of a broken string, there should be one special direction, which is where the string is located. Why didn't we see it in electrons? Or is the string is in another dimension so the charge looks the same from all directions in 3D space?

This post imported from StackExchange Physics at 2015-05-14 21:18 (UTC), posted by SE-user CliffX

Answer 1

In string-net theory, the density of the (oriented) string is a vector field $\vec E$. If string are all closed strings with no end, then $\vec \partial \cdot \vec E =0$. So the ends of the string are the source of $\vec E$, and correspond to the charge. The ends of strings are always discrete, impying that the charge is quantized. i.e. one end = charge-1.

Comments

How about the 2nd question? Does it make sense?