Help with a paper on semiclassical strings in anti-desitter space

[snypehype46]

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Help with a paper on semi-classical strings

Hi, I was given the task to read this paper https://arxiv.org/abs/hep-th/0204051 entitled "A semi-classical limit of the gauge/string correspondence" by Polyakov. On page 7 of this paper it is mentioned that the maximal radial coordinate of the string is p0 and that the string is constrained by the equation coth^2 p0 = w^2 (equation number 16 in the paper). However, I have no idea on why that would hold and why is true. Could anyone enlighten me on this?

 

[AndyW]

Hello,

Thank you for bringing up this question about the paper by Polyakov. The equation coth^2 p0 = w^2 (equation number 16) is a result of the semi-classical limit of the gauge/string correspondence. In this limit, the string is approximated as a classical object, and the radial coordinate p0 represents the maximal distance the string can reach. This distance is determined by the tension of the string and the energy of the system, which is represented by the parameter w in the equation.

To understand why this equation holds, it is helpful to look at the derivation in the paper. The authors use the action principle to find the classical equations of motion for the string. These equations involve the string tension and an energy term, which is proportional to the parameter w. By solving these equations, the authors are able to determine the maximal radial coordinate p0 of the string.

In short, the equation coth^2 p0 = w^2 is a result of the classical dynamics of the string in the semi-classical limit. It represents the balance between the tension of the string and the energy of the system. I hope this explanation helps clarify your confusion. Please let me know if you have any further questions.