Undergrad Fundamental equation in string theory

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There is currently no known fundamental equation in string theory from which all properties can be derived. The Polyakov action is often referenced as a key equation, facilitating easier quantization of string theory. However, while it serves as a foundation for perturbative string theory, it does not adequately address non-perturbative aspects. The supersymmetrization of the Polyakov action is also important in this context. Overall, the quest for a comprehensive fundamental equation in string theory remains unresolved.
kent davidge
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Is there a fundamental equation in string theory and can it be derived from a variational principle?
 
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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.
 
kent davidge said:
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.
 
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The Polyakov action (or its supersymmetric generalization) is fundamental for perturbative string theory, but it is not sufficient to understand the non-perturbative aspects.
 
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