String theory, string dimensions?

[Nav]

Strings are said to be one dimensional, due to the math. And I understand that there are problems in the math when they put the strings in 3 or 2 dimensions.
According to string theory, lengths smaller than Planck length have no physical significance.
Could it be that strings are 3 dimensional but their height and width dimensions are so small and insignificant they they cannot be taken into consideration or calculated by the mathematics?

 

[Dr. Courtney]

Sure it could be. String theory is so far from making much in terms of verifiable predictions that anything is possible.

The word "theory" is only loosely applicable to the body of hypothetical work associated with strings.

 

[bapowell]

Strings are said to be one dimensional, due to the math. And I understand that there are problems in the math when they put the strings in 3 or 2 dimensions.
According to string theory, lengths smaller than Planck length have no physical significance.
Could it be that strings are 3 dimensional but their height and width dimensions are so small and insignificant they they cannot be taken into consideration or calculated by the mathematics?

It has not been possible to construct a quantum theory of objects having more than 1 dimension.

 

[Demystifier]

It has not been possible to construct a quantum theory of objects having more than 1 dimension.

Higher dimensional branes can be quantized too, but this leads to UV divergences. Still, one can always tame these divergences by regularization and renormalization.

 

[Nav]

Higher dimensional branes can be quantized too, but this leads to UV divergences. Still, one can always tame these divergences by regularization and renormalization.

Are you saying that it is possible for strings to have higher dimensions like branes?

 

[bapowell]

Higher dimensional branes can be quantized too, but this leads to UV divergences. Still, one can always tame these divergences by regularization and renormalization.

I see. I thought it had something to do with stability: http://www.sciencedirect.com/science/article/pii/0550321389902149

 

[Nav]

I see. I thought it had something to do with stability: http://www.sciencedirect.com/science/article/pii/0550321389902149

A string can still have three dimensions it's just that those other two dimensions are insignificant.
It comes down to actual dimensions. 1-D is a mathematical convenience that often works if the size in 1 dimension is much larger than the other two.
Think of a real guitar string. If it is 24" long, but only 0.005" in diameter, a 1-D model is a good approx.

 

[Nav]

I see. I thought it had something to do with stability: http://www.sciencedirect.com/science/article/pii/0550321389902149

The other dimensions of the string are too small to be taken into account by the calculations and therefore are just portrayed to be one dimensional.
Branes are different, you can't construct a quantum theory on branes because all of its dimensions are taken into account by the calculations because they are so big.

 

[bapowell]

A string can still have three dimensions it's just that those other two dimensions are insignificant.
It comes down to actual dimensions. 1-D is a mathematical convenience that often works if the size in 1 dimension is much larger than the other two.
Think of a real guitar string. If it is 24" long, but only 0.005" in diameter, a 1-D model is a good approx.

I understand that a 3-dimensional object can look 1-dimensional, but these objects behave very differently when quantized. Are you saying that it is possible to quantize a 3-dimensional object without stability issues or other problems? In string theory, the other dimensions are not simply ignored -- the string is not "portrayed to be one dimensional" -- it actually is, exactly.

 

[Nav]

I understand that a 3-dimensional object can look 1-dimensional, but these objects behave very differently when quantized. Are you saying that it is possible to quantize a 3-dimensional object without stability issues or other anomalies? In string theory, the other dimensions are not simply ignored -- the string is not "portrayed to be one dimensional" -- it actually is, exactly.

I never said that they are ignored, what i meant was that the other dimensions are too small to be considered in the calculations

 

[bapowell]

I never said that they are ignored, what i meant was that the other dimensions are too small to be considered in the calculations

Right, and I'm saying this is wrong. The strings of string theory are *exactly* 1-dimensional. If you add more dimensions, the quantization procedure is very different.

 

[Demystifier]

Are you saying that it is possible for strings to have higher dimensions like branes?

No.

 

[haushofer]

Higher dimensional branes can be quantized too, but this leads to UV divergences. Still, one can always tame these divergences by regularization and renormalization.

Could you give a link where this is done or discussed?

 

[Demystifier]

Could you give a link where this is done or discussed?

I don't know a specific reference, but it looks obvious. First quantization of a p-brane is essentially a quantum (p+1)-dimensional field theory, which in general leads to UV divergences (p=1 is exception due to the large group of conformal symmetry). Each UV divergent field theory can be renormalied in the sense of an effective theory.

 

[bapowell]

I don't know a specific reference, but it looks obvious. First quantization of a p-brane is essentially a quantum (p+1)-dimensional field theory, which in general leads to UV divergences (p=1 is exception due to the large group of conformal symmetry). Each UV divergent field theory can be renormalied in the sense of an effective theory.

But what about the free field theory? I understand "UV divergences" only in the context of interactions.

 

[samalkhaiat]

The other dimensions of the string are too small to be taken into account by the calculations and therefore are just portrayed to be one dimensional.
Branes are different, you can't construct a quantum theory on branes because all of its dimensions are taken into account by the calculations because they are so big.

Can you show me those "calculations"?

 

[Demystifier]

But what about the free field theory? I understand "UV divergences" only in the context of interactions.

Even for free theory there is a UV infinite energy of the ground state, but this can always be removed by normal ordering.

 

[haushofer]

I don't know a specific reference, but it looks obvious. First quantization of a p-brane is essentially a quantum (p+1)-dimensional field theory, which in general leads to UV divergences (p=1 is exception due to the large group of conformal symmetry). Each UV divergent field theory can be renormalied in the sense of an effective theory.

Ah, ok, I understood your statement in the sense that these qft's are fully renormalizible.

 

[bapowell]

Even for free theory there is a UV infinite energy of the ground state, but this can always be removed by normal ordering.

Right, but those are just the normal divergences we find with any free quantum field theory. I had always read that there were stability issues when attempting to quantize fundamental objects of dimension greater than 1.

 

[Demystifier]

I had always read that there were stability issues when attempting to quantize fundamental objects of dimension greater than 1.

Can you give a reference on that stability issues?

 

[bapowell]

Can you give a reference on that stability issues?

http://www.sciencedirect.com/science/article/pii/0550321389902149