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I am trying to reproduce derivation of the Born-Infeld (BI) action for D-branes as it is presented in

R.J. Szabo, BUSSTEPP Lectures on String Theory, arXiv:hep-th/0207142.

In particular, I don't understand how the inverse Green function $N^{-1}$ of the Laplace equation appears in the boundary action (page 70 eq. 7.29)

$$ S_{\rm b}[\xi, A] ~=~\frac{1}{2} \int_0^{2\pi} \! \mathrm{d}\theta \left( \frac{1}{2\pi\alpha^{\prime}}\xi^{\mu} N^{-1}\xi_{\mu} + \mathrm{i}F_{\mu\nu} \xi^{\mu}\dot{\xi}^{\nu}\right). \tag{7.29} $$ Can anyone explain it?

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  • $\begingroup$ You might find more details from the original derivation in the paper “Non-linear electrodynamics from quantized strings” by E.S. Fradkin and A.A. Tseytlin. $\endgroup$ – Sparticle Sep 16 '18 at 9:59

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