I Fundamental equation in string theory

[kent davidge]

Is there a fundamental equation in string theory and can it be derived from a variational principle?

 

[Demystifier]

If you mean an equation from which all properties of string theory can, in principle, be deductively derived, then such an equation is not yet known.

 

[haushofer]

Is there a fundamental equation in string theory and can it be derived from a variational principle?

If there is "a" fundamental equation at all in string theory, I guess you're looking for the Polyakov action,

https://en.wikipedia.org/wiki/Polyakov_action

This is basically a rewritten Nambu-Goto action such that quantization becomes easier. For the full string theory, you want the supersymmetrization of this Polyakov-action.

 

[Demystifier]

The Polyakov action (or its supersymmetric generalization) is fundamental for perturbative string theory, but it is not sufficient to understand the non-perturbative aspects.

 

[Urs Schreiber]

Is there a fundamental equation in string theory and can it be derived from a variational principle?

This is an FAQ: see What are the equations of string theory?