Why point particle interaction has UV divergence,but string interaction does not?

[ndung200790]

Please teach me this:
Why point particle interaction(QTF theory) has UV divergences,but string interaction does not have UV divergences.Because I think that calculating the probability amplitude of a process,we must sum(or integrate) over all possible value of momentum.So how we avoid the UV divergence?
Thank you very much in advance.

 

[suprised]

Because I think that calculating the probability amplitude of a process,we must sum(or integrate) over all possible value of momentum

That is true in particle QFT, but not in string theory. What replaces momentum integration is an integration over the moduli space ("shapes") of Riemann surfaces, and this is substantially different to particle theory. One may loosely say there appears a UV cutoff for the momentum integration. Actually things are more complicated and the stringy way of integration is more than a cutoff, and thus cannot be expressed in terms of particle QFT supplemented by a naive momentum cutoff. Pertaining to the geometry of Riemann surfaces, there are notions like modular invariance which have no analog in particle physics, so string theory is "more" than just a collection of infinitely many particle theories. That's why it can do things that cannot be achieved in particle QFT.

 

[Orbb]

One thing I have always wondered in this context is what happens when one talks about the scattering of D0-branes, which are pointlike objects. In that case, no smearing out of the interaction vertices occurs, as it does for extended objects like strings. So doesn't this bring short-distance divergences back into the game?

 

[suprised]

One thing I have always wondered in this context is what happens when one talks about the scattering of D0-branes, which are pointlike objects. In that case, no smearing out of the interaction vertices occurs, as it does for extended objects like strings. So doesn't this bring short-distance divergences back into the game?

Yes, from open strings stretched between the branes, which become massless when the branes coincide. So in a sense these are on-shell divergences.