# The limit (R -> 0) of type IIA superstrings is equivalent

1. Apr 7, 2010

### wam_mi

The limit (R --> 0) of type IIA superstrings is equivalent

Hi there,

The limit (R --> 0) of type IIA superstrings is equivalent to the limit (R --> infty) of type IIB theory. Could someone explain how this works?

Thanks

2. Apr 7, 2010

### Naty1

Re: T-Duality

Here's a conceptual descirption: Ed Witten dsisovered a new type of duality....It seems that a strong coupling constant in any of the five major string theories has a dual description in terms of a weak coupling behavior of another....for example as the Type IIA string coupling constant is increased strings expand from a one dimensional loop (circle) to a three dimensional torus (bicycle inner tube shape)..

Briane Green goes over maybe 20 pages of how this was discovered and what it means in non mathematical terms in THE ELEGANT UNIVERSE, beginning around page 297, Chapter 12.

I don't know the math involved but I do understand most of string theory is still perturbative...meaning approximation schemes are used to solve complex equations...and the applicability of perturbative solutions is apparently not entirely clear to theorists....what they mean and when they apply requires certain assumptions....its all part of the "fog" of string theory calculations....
hope that helps a little.

Last edited: Apr 7, 2010
3. Apr 7, 2010

### tom.stoer

Re: T-Duality

Right, but this strong-weak duality is called S-duality.

The idea for T-duality is rather simple: think about cylinder (radius r) with a string wrapped around. You can have winding modes where the energy grows with the radius (as the tension increases) and you can have vibration modes. Now if the size of the cylinder changes from r to R²/r the energy of the winding modes decreases whereas the energy of the vibration modes increases. For this particular change of the radius (depending on R) the change from r to R²/r does not affect the overall spectrum which is the sum of the winding + the vibrating energy.

So it's basically the description of the string that changes; but this unobservable (!) change of the description does not affect the physical observable, the Hamiltonian (energy). There is no physical experiment that is able to distinguish between these two descriptions.