Due to the string-theory tag, I presume that you're asking about something like Braneworld scenarios. |
Brane-world scenarios refer to lower dimensional branes (or rather, worldvolumes) suspended in a higher dimensionaln spactimes, e.g. 4-dimensional world - volumes suspended in an 11 - dimensional spacetime.
A prominent example of a brane - world scenario is the Randall - Sundrum Brane - World Scenario.
To quote the abstract of the linked paper:
Conventional wisdom states that Newton's force law implies only four non-compact dimensions. We demonstrate that this is not necessarily true in the presence of a non-factorizable background geometry. The specific example we study is a single 3-brane embedded in five dimensions. We show that even without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and general relativistic gravity is reproduced to more than adequate precision.
In other words, they show that general relativity is still around the same in such a brane - world scenario.
But what about the other forces?
Remember, the standard model interactions are generally open strings, so they' (with Dirchilet boundary conditions) are bound to the branes.
So, they'll only transverse across the branes, and therefore, Q.E.D.
Now, coming to your questions...
I interpret your question as:
Can there be an embedded brane (or world-volume) in our space (or spacetime)?
If there can be those bosonic embedding functions $X^\mu$ for the embedding of a $p$-brane's $p+1$-dimensional world - volume in a higher dimensional spacetimme, then there probably could be such a brane in our spacetime too, right ? .
And there certainly is : ) Any brane in our spacetime would probably satisfy the question.