Fundamental equation in string theory

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SUMMARY

The fundamental equation in string theory is not yet established, with no known equation from which all properties can be derived. The Polyakov action, a reformulation of the Nambu-Goto action, facilitates quantization and is essential for perturbative string theory. However, it is insufficient for understanding non-perturbative aspects. For a comprehensive understanding, one must also consider the supersymmetrization of the Polyakov action.

PREREQUISITES
  • Understanding of the Polyakov action
  • Familiarity with the Nambu-Goto action
  • Knowledge of perturbative and non-perturbative string theory
  • Basic principles of variational principles in theoretical physics
NEXT STEPS
  • Research the supersymmetrization of the Polyakov action
  • Study the implications of the Nambu-Goto action in string theory
  • Explore non-perturbative aspects of string theory
  • Examine variational principles in theoretical physics
USEFUL FOR

The discussion is beneficial for theoretical physicists, string theorists, and advanced students seeking to deepen their understanding of string theory and its foundational equations.

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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