# Non-perturbative theory and perturbative theory

1. Aug 18, 2010

### micomaco86572

Why is the string theory said to be a perturbative theory, while the LQG is a non-perturbative theory?

2. Aug 18, 2010

### Kevin_Axion

3. Aug 18, 2010

I do not think string theory is perturbative. Many crucial phenomena in string theory like the existence of D-branes, S-duality, AdS/CFT and so on are non-perturbative.

4. Aug 18, 2010

### Kevin_Axion

String theory is perturbative, S-Duality, D-branes and AdS/CFT Correspondence stem from Superstring Theory - a Perturbation Theory

5. Aug 18, 2010

Look at this review,

"An Introduction to Non-perturbative String Theory", Ashoke Sen

http://arxiv.org/abs/hep-th/9802051

It reviewed the non-perturbative part of string theory which was new at that time and now becomes the familiar parts of textbooks.

6. Aug 18, 2010

For example, by using perturbative series, you will never get S-duality because one side has coupling g and the other side has coupling 1/g, so perturbative series can at most work on one side and cannot see the equivalence.

7. Aug 18, 2010

### Kevin_Axion

8. Aug 18, 2010

My viewpoint is that now things change. 20 years ago, we only knew that string theory was describing the perturbation around a fixed background and it is true that before 1995, majority of string theory formulation was perturbative. But now with the dramatic developments, especially AdS/CFT, we see that string theory describes both the perturbative region and the non-perturbative region. The string perturbative series loses its importance in string theory.

9. Aug 18, 2010

### Kevin_Axion

Yes, I absolutely agree that Superstring Theory is becoming more non-perturbative with the development of M-Theory, Gauge-Gravity Dualities (AdS/CFT, dS/CFT, Kerr/CFT...), Symmetries in nature/mathematics as well as various String Dualities. What I'm trying to say is that the core of Superstring theory, pre-1995/1997, was mostly perturbative.

10. Aug 18, 2010

### micomaco86572

stupid question: why a perturbative theory cannot be background independant? thx.

11. Aug 18, 2010

### Kevin_Axion

12. Aug 18, 2010

Thx Kev!