Open Strings, D-Branes, and Conservation of Energy

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SUMMARY

String theories that incorporate open strings inherently require the presence of closed strings to uphold the principle of conservation of energy. An open string not connected to a closed string risks losing energy at its endpoints, which necessitates the inclusion of closed strings in the framework. D-branes, which are crucial in string theory, can be conceptualized as entities that interact with both open and closed strings. The equivalence of one-loop open-string diagrams and tree closed-string diagrams further illustrates the interconnectedness of these concepts.

PREREQUISITES
  • Understanding of string theory fundamentals
  • Familiarity with D-branes and their role in string theory
  • Knowledge of energy conservation principles in theoretical physics
  • Basic grasp of topological equivalence in diagrams
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  • Explore the relationship between open strings and closed strings in string theory
  • Study the properties and functions of D-branes in string theory
  • Investigate the implications of energy conservation in quantum field theories
  • Learn about topological aspects of string diagrams and their equivalences
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The discussion is beneficial for theoretical physicists, string theorists, and advanced students interested in the intricate relationships between open and closed strings, as well as the implications for energy conservation in string theory.

Keys
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Can someone please explain to me why string theories with open strings must also have closed strings? I've read it is due to conservation of energy, an open string not attached to a closed string will lose it's energy off an end. Does this mean all D-branes must be made from closed strings? I can easily imagine open strings attached to each other in a manner which does not allow loose ends and doesn't require closed strings.
 
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Keys said:
Can someone please explain to me why string theories with open strings must also have closed strings?
An easy (though far from rigorous) way to see this is as follows:
A one-loop open-string diagram is topologically the same as a tree closed-string diagram. Try to convince yourself by drawing it!
 
OK, if they look the same, then they are considered equivalent? What's the point in specifying then? This leads to my 2nd question, if a one loop open string is attached to a d-brane, I've read it cannot be detached. But if we can just relabel it a tree closed string, then it is detachable? Thanks.
 

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