A Slant on Warped Extra Dimensions

[suprised]

Just a simple question about your first comment which is somewhat mysterious to me: I always thought conformal invariance was somehow thightened to 2 d unless you use Weyls trick of course.

True… now I understand what your aim is. The issue is not to quantize the world-volume of general branes, for which indeed there is all sorts of problems. Specifically D-branes are "dual" representatives of branes that can be represented perturbatively, which means in terms of 2d CFT with boundaries. So the trick behind D-branes is that instead quantizung solitonic world-volumes, one can describe the non-perturbative closed string dynamics by perturbative open strings based on boundary CFTs, and similar computational techniques can then be applied as for closed strings.

Note that not all p-branes are equivalent to D-branes, like the NS fivebrane, and for those these methods fail.

 

[Careful]

True… now I understand what your aim is. The issue is not to quantize the world-volume of general branes, for which indeed there is all sorts of problems. Specifically D-branes are "dual" representatives of branes that can be represented perturbatively, which means in terms of 2d CFT with boundaries. So the trick behind D-branes is that instead quantizung solitonic world-volumes, one can describe the non-perturbative closed string dynamics by perturbative open strings based on boundary CFTs, and similar computational techniques can then be applied as for closed strings.

Note that not all p-branes are equivalent to D-branes, like the NS fivebrane, and for those these methods fail.

Well, as I said, I do not know enough details to make a definite statement about string theory (I studied it only intensely for like three months) ; I can only judge it from the perspective where I am standing (about the other approaches like CDT, LQG and causal set, I do know all the fine print). Actually, the reason why I would say that my approach is not so far from string is because it treats gravity in a similar dual way and insights such as the holographic principle appear to show up directly (also, my black holes do not have an horizon, so they are not perfectly black). On the other hand, the geometry and quantum theory I develop is far more general (and sophisticated) and locality on spacetime is a sacred principle for me (altough the construction is nonlocal on the tangent bundle). So, we will see what happens in the future...

Careful