Meaning of area in the Nambu Goto string action

In summary, there is confusion about which area is being minimized in the Nambu-Goto action, either in the target space or in the parameter space. From Zwiebach's book, it appears that the area is being constructed in the target space, with derivatives being taken with respect to the parameters. However, in David Tong's notes, it seems that the area is being built in the worldsheet rather than the target space. Tong refers to the pullback of the flat Minkowskian metric on the worldsheet, which is the restriction to the worldsheet. It is believed that these two concepts are equivalent in differential geometry.
  • #1
clerk
20
0
I am confused about what area is being minimised in the nambu goto action..the one in the target space or the one in the parameter space? From Zwiebach's book I think he is trying to construct the area in target space and in the process we get derivatives with respect to parameters since each co-ordinate in the target space is now a function of the two parameters.. But reading David Tong's notes, it seems he is building the area in the worldsheet rather than in target space...because he talks about pullback of the flat minkowskian metric on the worldsheet.. (by worldsheet i think he means the parameter space?)
 
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  • #2
I think they are doing the same thing. By world sheet Tong means the image, and the pullback of the metric is the restriction to the world sheet. So in both cases it is area in the target space.
 
  • #3
afaik these two concepts are strictly equivalent in differential geometry
 

1. What is the Nambu Goto string action?

The Nambu Goto string action is a mathematical framework used to describe the dynamics of a string. It is based on the concept of a string being a one-dimensional object with tension, and its motion is described by a two-dimensional surface embedded in a higher-dimensional space.

2. What does the area in the Nambu Goto string action represent?

In the Nambu Goto string action, the area represents the energy of the string. This is because the tension in the string is proportional to its energy, and the area is a measure of the string's length, which is related to the tension.

3. How is the Nambu Goto string action related to string theory?

The Nambu Goto string action is the simplest and most fundamental action used in string theory. It is the starting point for understanding the dynamics of strings in string theory and is used to derive the equations of motion for the strings.

4. What is the significance of the Nambu Goto string action in physics?

The Nambu Goto string action is significant because it provides a way to describe the behavior and interactions of strings in a mathematical framework. This is important in physics as strings are believed to be the fundamental building blocks of the universe and understanding their behavior is essential in developing a theory of everything.

5. Are there any limitations or criticisms of the Nambu Goto string action?

While the Nambu Goto string action is a useful tool in string theory, it has been criticized for its inability to incorporate certain physical phenomena, such as string interactions and quantum effects. It also does not take into account the curvature of spacetime, which is necessary for a complete description of gravity. However, it remains a valuable starting point for understanding the dynamics of strings in string theory.

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