Non-perturbative theory and perturbative theory

[micomaco86572]

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

 

[Kevin_Axion]

Because most of the calculations are done in terms of a Power Series, or infinite summations (therefore the calculations are "approximate solutions") : http://en.wikipedia.org/wiki/Perturbation_theory

 

[Cadmium]

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.

 

[Kevin_Axion]

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

 

[Cadmium]

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.

 

[Cadmium]

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.

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

 

[Kevin_Axion]

There are non-perturbative aspects to String Theory but the majority of its formulation is perturbative, read the section on background independence: http://en.wikipedia.org/wiki/String_theory#Background_independence

 

[Cadmium]

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.

 

[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.

 

[micomaco86572]

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

 

[Kevin_Axion]

This will answer your question: http://en.wikipedia.org/wiki/Background_independence#Manifest_background-independence

 

[micomaco86572]

Thx Kev!