Can 3D String Theory Overcome UV Divergences Found in 1D String Theory?

[PhilosophyofPhysics]

I was wondering if anyone has ever tried to formulate a string theory with a 3D string rather than a 1D string. Has this been done? Is this much more complicated?

 

[Keys]

I guess you've never noticed all this talk of branes or membranes.

 

[PhilosophyofPhysics]

Well...
Branes are not what I'm thinking about unless a 3D string is equivalent to a 3 brane. I've read the first half of Zwiebach, but I might have forgot about the part where he said a 1 D brane was a string.

Anyway, I'm thinking kind of a real string with width, height and length but just exceedingly small.

 

[Demystifier]

What you are talking about is a small 3-brane. One can formulate such a theory, but unlike the string theory (1-brane), the quantum theory contains UV divergences that cannot be eliminated, at least not perturbatively. In fact, UV divergences can be (perturbatively) eliminated only for objects extended in 1 dimension (not 0, not 2, ...), which is related to the fact that the conformal group in 2 dimensions (the other dimension is due to the extension in time) is much reacher than in other numbers of dimensions.