Open Strings, D-Branes, and Conservation of Energy

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In summary, string theories with open strings must also have closed strings due to the conservation of energy. This means that all D-branes must be made from closed strings. This is because a one-loop open-string diagram is topologically equivalent to a tree closed-string diagram. This also implies that a one-loop open string, if attached to a D-brane, cannot be detached. However, it can be relabeled as a tree closed string and then be detached.
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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!
 
  • #3
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.
 

FAQ: Open Strings, D-Branes, and Conservation of Energy

What are open strings and D-branes?

Open strings are fundamental objects in string theory that have two endpoints and can propagate through spacetime. D-branes are extended objects that open strings can end on, and they play a crucial role in the dynamics of string theory.

How are open strings and D-branes related to each other?

Open strings can end on D-branes, which means the endpoints of the open string are attached to the D-brane. D-branes can also interact with each other by exchanging open strings. This interaction is essential in understanding the behavior of D-branes in string theory.

What is the significance of open strings and D-branes in string theory?

Open strings and D-branes are crucial in understanding the dynamics of string theory. D-branes give us a way to describe how strings interact with each other and how they propagate through spacetime. They also provide a connection between string theory and other physical theories, such as gauge theories.

Can open strings and D-branes be experimentally tested?

At the moment, there is no experimental evidence for open strings and D-branes. However, there are ongoing efforts to test string theory through indirect methods, such as studying the cosmic microwave background radiation and particle colliders. These experiments may provide evidence for the existence of open strings and D-branes.

Are there any practical applications of open strings and D-branes?

Currently, there are no direct practical applications of open strings and D-branes. However, the study of string theory has led to developments in mathematics and theoretical physics, which can have potential future applications. Additionally, the study of string theory can help us better understand the fundamental laws of nature.

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