$U(1)$ 5-dimensional Kaluza-Klein topological defects Five-dimensional Kaluza-Klein theory is well-known to predict that the electromagnetic field can be described as a curled additional dimension over four-dimensional spacetime. That is, you only need General Relativity, and an additional curled circular dimension to obtain a vector massless field that fits the bill to describe electromagnetism
For instance, if we can describe local KK spacetime as a fiber $U(1) \times M^4$, and if we imagine pictorically the $M^4$ as a hose length, then the $U(1)$ fiber is like the hose thickness
Something that I'm curious is, under this theory, what would be the expected behaviour of simple defects on the topology.
One defect In particular that I want to consider is the hose pictorial image, but joining a new hose leg to an existing hose, basically producing a hose with 3 legs (or a 3-legged pant, if you prefer). In this case, the fiber on top of $M^4$ would be $U(1)$ only in the region far from the defect. Another way to depict this is imagining a T, and our $M^4$ universe is the upper arm of the T.
How would such defect look in our side of the universe? How would the electromagnetic field look near such a defect that significantly alters the simple $U(1)$ topology?
 A: As I understand it your question implies that the "hose" is at some region in $M^4$, this picture is allowed if you consider your $X\times M^4$ embedded in 6-dimensional space, however it doesn't make sense to say the topology of a loop (1 compact dimension) can turn from one loop into two...
You can have local changes in the radius of this loop, this is due to a non-constant dilaton (fluctuations thereof called "radion"). If this loop is not circular anymore then you loose your $U(1)$ isometry, and with it your massless gauge field.
However let's entertain this possibility, that there is some embedding into 6-dimensional space and the "hose" is splitting. This would physically mean that the 4-dimensional universe is splitting into two in regions of (pre-split) space-time where this split happens. Near this split, the compact extra dimension cannot be circular anymore, so that I would guess that the $U(1)$ gauge field acquires a mass, soon after to loose it once well into the new universe and circularity is resotred.
Note: discussion with ACuriousMind helped refine the answer, see comments.
