Fundamental equation in string theory

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Discussion Overview

The discussion centers on the existence of a fundamental equation in string theory and whether it can be derived from a variational principle. Participants explore the implications of such an equation for both perturbative and non-perturbative aspects of string theory.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants suggest that a fundamental equation from which all properties of string theory can be derived is not yet known.
  • One participant proposes the Polyakov action as a candidate for a fundamental equation, noting its role in simplifying quantization compared to the Nambu-Goto action.
  • Another participant emphasizes that while the Polyakov action is fundamental for perturbative string theory, it does not adequately address non-perturbative aspects.
  • A later reply references an FAQ regarding the equations of string theory, indicating that this topic is commonly discussed.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the existence of a singular fundamental equation in string theory, and multiple competing views regarding the role of the Polyakov action and its limitations are presented.

Contextual Notes

There are limitations in the discussion regarding the definitions of "fundamental equation" and the scope of string theory being considered, particularly in distinguishing between perturbative and non-perturbative frameworks.

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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