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  How to 'read' a coupling from given action?

+ 2 like - 0 dislike

This is some kind of a 'stupid' question from a undergraduate.

I have read some works on supergravity and string theory, and I'm curious about how can we 'read' coupling from given action and calculate interaction potential energy from it.

For example, from the brane action:

\(S=-T_p \int d^{p+1}\sigma (1+\frac{\alpha(p)\phi}{2}+\frac{1}{2}\eta^{\mu \nu}h_{\mu \nu})-\frac{T_p}{(p+1)!}\int d^{p+1}\sigma \epsilon^{\alpha_0\alpha_1...\alpha_p}A_{\alpha_0\alpha_1...\alpha_p}\)

we can 'read' coupling:

\(J_{h}^{(i)}=-c_pV_{p+1}N_i\eta^{\mu \nu}h_{\mu \nu}\) for graviton,and some more for others.

and with this, we can calculate the potential energy due to graviton:

\(U_h=J_h^{(1)} J_h^{(2)}\)

(I can't type it on tex, but there should be a horizontal brace under two Js)

for more details, plz go to http://arxiv.org/abs/1409.0969, this is an example of my deacription.

Thank you very much for your answer.

asked Jun 7, 2015 in Theoretical Physics by mcstring (10 points) [ no revision ]

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